Access to this full-text is provided by Copernicus Publications on behalf of European Geosciences Union.
Content available from Biogeosciences
This content is subject to copyright.
Biogeosciences, 20, 3093–3117, 2023
https://doi.org/10.5194/bg-20-3093-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
Potassium limitation of forest productivity – Part 1: A mechanistic
model simulating the effects of potassium availability on canopy
carbon and water fluxes in tropical eucalypt stands
Ivan Cornut1,2,5, Nicolas Delpierre1,3, Jean-Paul Laclau2,5, Joannès Guillemot2,4,5, Yann Nouvellon2,6,
Otavio Campoe6, Jose Luiz Stape7, Vitoria Fernanda Santos8, and Guerric le Maire2,5
1Université Paris-Saclay, CNRS, AgroParisTech, Ecologie Systématique et Evolution, Orsay, France
2CIRAD, UMR Eco&Sols, Montpellier, France
3Institut Universitaire de France (IUF), Paris, France
4Department of Forest Sciences ESALQ, University of São Paulo, Piracicaba, SP, Brazil
5Eco&Sols, University of Montpellier, CIRAD, INRAe, Institut Agro, IRD, Montpellier, France
6Departmento de Ciências Florestais, Universidade Federal de Lavras, Lavras, MG, Brazil
7Department of Forest Science, São Paulo State University, Botucatu, SP, Brazil
8Suzano Papel e Celulose, Salvador, BA, Brazil
Correspondence: Ivan Cornut (ivan.cornut@cirad.fr)
Received: 5 September 2022 – Discussion started: 9 September 2022
Revised: 28 April 2023 – Accepted: 10 May 2023 – Published: 31 July 2023
Abstract. The extent of the potassium (K) limitation of for-
est productivity is probably more widespread than previously
thought, and K limitation could influence the response of
forests to future global changes. To understand the effects
of K limitation on forest primary production, we have devel-
oped the first ecophysiological model simulating the K cycle
and its interactions with the carbon (C) and water cycles. We
focused on the limitation of the gross primary productivity
(GPP) by K availability in tropical eucalypt plantations in
Brazil. We used results from stand-scale fertilisation experi-
ments as well as C flux measurements in two tropical euca-
lypt plantations to parameterise the model. The model was
parameterised for fertilised conditions and then used to test
for the effects of contrasting additions of K fertiliser. Sim-
ulations showed that K deficiency limits GPP by more than
50 % during a 6-year rotation, a value in agreement with es-
timations in K-limited eucalypt stands. Simulations showed
a decrease of modelled canopy transpiration of around 50 %
and a decrease in modelled water-use efficiency WUEGPP of
10 %. Through a sensitivity analysis, we used the model to
identify the most critical processes to consider when studying
K limitation of GPP. The inputs of K to the stands, such as the
atmospheric deposition and weathering fluxes, and the reg-
ulation of the cycle of K within the ecosystem were critical
for the response of the system to K deficiency. Litter leaching
processes were of lower importance, since residence time of
K in litter was low. The new forest K-cycle model developed
in the present study includes multiple K processes interact-
ing with the carbon and water cycles, and strong feedbacks
on GPP were outlined. This is a first step in identifying the
source or sink limitation of forest growth by K.
1 Introduction
Nutrient limitation of plant growth has been well established
since the 19th century (von Liebig, 1840). Several macro-
(N, K, P) or micro-nutrients can limit the growth of plants
(Townsend et al., 2011). The nitrogen (N), phosphorus (P),
and potassium (K) limitation of plant growth is a well es-
tablished phenomenon, as demonstrated by the widespread
use of NPK fertilisers in agriculture. It has however less
extensively been studied in natural ecosystems. This prob-
ably stems from the fact that, contrary to agrosystems where
field trials are currently set up to select the best fertilisa-
tion regimes, natural ecosystems, and particularly forests,
Published by Copernicus Publications on behalf of the European Geosciences Union.
3094 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
are rarely fertilised. Counter-examples in forestry include
lime application trials (Bonneau, 1972; Guitton et al., 1988;
Rocha et al., 2019) and other fertilisation trials (Hyvönen
et al., 2008). This limitation of primary production by nu-
trients will get more palpable as the atmospheric concentra-
tion of CO2, one of the substrates limiting photosynthesis,
increases (Ellsworth et al., 2022).
N and P are generally considered to be the most limiting
elements for global forest growth, with no clear geograph-
ical pattern for either N nor P limitation (Du et al., 2020;
Cunha et al., 2022; Manu et al., 2022; Hou et al., 2020).
This paradigm neglects other macro- and micro-nutrients
as causes of limitation or co-limitation. In the tropics, evi-
dence from eucalypt plantations in Brazil suggests that K and
micro-nutrients are often the primary limiting elements for
productivity (Silveira et al., 2000; Cornut et al., 2021). More
generally, the K limitation of forest growth appears to be a
widespread phenomenon, which has been overlooked so far
(Tripler et al., 2006; Sardans and Peñuelas, 2015). Beyond
its role on forest growth, K is also an element of geopolitical
importance (Nardelli and Fedorinova, 2021), since it is an es-
sential component of most agricultural fertilisers, and potash
sources are spread among few countries (Prakash and Verma,
2016).
Despite its importance for forest ecosystems, few models
have so far been developed to investigate the K cycle in forest
ecosystems. Some models focused on the impact of anthro-
pogenic perturbations and management on multiple nutrient
cycles in plants (e.g. wheat; Johnson et al., 2000) and, among
them, on the cycle of K in temperate forests (e.g. models
NuCM; Liu et al., 1992; ForNBM; Zhu et al., 2004). Potas-
sium models for annual crops have also been developed and
have focused mainly on the K dynamics in soils and uptake
by the plants (Seward et al., 1990; Silberbush and Barber,
1984). To the best of our knowledge, only one K model, de-
veloped for arable crops, has to date formalised the link be-
tween K availability and plant productivity, through an em-
pirical relationship (Greenwood and Karpinets, 1997). This
feedback had previously been deemed necessary to predict K
uptake more accurately (Seward et al., 1990). Beside these
studies, which explicitly modelled the ecosystem K cycle at
a broad scale, some papers have quantified through ecophys-
iological modelling the sensitivity of ecosystem functioning
to the availability of K. For example, the influence of K on
the gross primary productivity (GPP) (Christina et al., 2015)
and water fluxes (Christina et al., 2018) of tropical eucalypt
plantations has been quantified with the MAESPA model, us-
ing a specific parameter set for each of the K fertilised and
non-fertilised treatments. In these works, the K cycle was not
explicitly modelled.
Modelling the various aspects of the ecosystem cycle of K
is a worthwhile endeavour, since K influences the ecosystem
water and carbon cycles in many ways in tropical eucalypt
plantations (Cornut et al., 2021) as well as in other forest
types (Sardans and Peñuelas, 2015; Tripler et al., 2006). In-
deed, K availability has a strong influence on the canopy pho-
tosynthesis (i.e. the source of carbon for the plant) through
its role on leaf development and senescence. Under low K
availability, leaf expansion is reduced by up to 30 % (Battie-
Laclau et al., 2013) and leaf lifespan is strongly reduced,
with estimated reductions from 25 % (Laclau et al., 2009)
up to 50 % (Battie-Laclau et al., 2013). The resulting loss in
leaf area, combined with K-deficiency anthocyanic (purple)
symptoms that diminish the leaves’ photosynthetic capacity
(Battie-Laclau et al., 2014a), leads to a strong reduction of
GPP (Epron et al., 2012). While it is more challenging to
study the activity of the plant’s carbon sinks (i.e. the trans-
port and use of carbohydrate molecules for the maintenance
of tissues, growth, the constitution of reserves, and defence;
Körner, 2015), there is evidence that assimilates’ transport
processes are also influenced by the availability of K. For ex-
ample, the loading and unloading of sugars from the phloem
are affected by K deficiency (Marschner et al., 1996), and,
more generally, the K nutritional status of the tree has an
impact on phloem sap mobility (Epron et al., 2016). Antho-
cyanic symptoms that develop on leaf margins could in par-
ticular be the consequence of the lower ability of K-deficient
leaves to export sugars into the phloem sap (Landi et al.,
2015). This body of evidence points towards a strong sink
limitation (mostly through the alteration of phloem export
capacity) of GPP under K limitation in addition to a source
limitation due to a reduced leaf area. More details relating to
the influence of K on these sink and source processes can be
found in Cornut et al. (2021). On the topic of the water cy-
cle, it has been shown that K concentration in the xylem sap
has an effect on the xylem conductivity (through a change of
xylem pit conductivity; Nardini et al., 2010). Potassium defi-
ciency also impacts stomatal functioning (Marschner, 2011),
but an absence of effect of K deficiency on intrinsic WUE has
been shown in tropical eucalypt stands (Epron et al., 2012;
Battie-Laclau et al., 2016).
The combined influences of K on C-source and C-sink
processes explain the K limitation of productivity. The
present study focuses on modelling the influence of K on
the C source (i.e. on GPP), which is based on the assump-
tion that C-source modelling would be the most straightfor-
ward step to start modelling the K limitation on productivity.
Indeed, process-based models of the C-source activity have
been developed for more than 4 decades (Farquhar et al.,
1980), which contrasts with models representing the activ-
ity of C sinks (e.g. Hölttä et al., 2006), which, while relevant
(e.g. Guillemot et al., 2017; Körner, 2015), are relatively new
and have not been validated at a large scale. While the N and
P limitation of GPP have been considered in models at scales
from the leaf to the globe (Thum et al., 2019; Goll et al.,
2012, 2017; Yang et al., 2014), no process-based model sim-
ulating the K cycle and its influence on GPP has been pub-
lished so far.
The objectives of the present study were thus to:
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3095
1. develop a model of the K biogeochemical cycle, cou-
pled to the carbon and water cycles, in forest ecosys-
tems;
2. evaluate the model using carbon and water flux data
measured at an eddy covariance site installed in a fer-
tilised (+K) tropical eucalypt plantation;
3. quantify the influence of K availability on the car-
bon (gross primary productivity, GPP) and water (evap-
otranspiration) ecosystem–atmosphere fluxes and on
the water-use efficiency of a tropical eucalypt stand,
through simulations in non-limited +K stands and
stands with omission of K fertiliser (oK),
4. conduct a sensitivity analysis of the model, with the aim
to identify the main processes responsible for the re-
sponse of GPP to the availability of K at the stand level.
To this end, we have developed a new K circulation mod-
ule in an existing ecophysiological forest model and repre-
sented the response of different physiological processes to
the availability of K in the plant. The model was param-
eterised and tested on two tropical eucalypt plantations in
Brazil. Because those ecosystems have a continuous phenol-
ogy, it required the creation of a leaf cohort model (see e.g.
Sainte-Marie et al., 2014) that explicitly takes into account
the effect of K on different leaf-level processes (leaf expan-
sion, lifespan, etc.).
2 Materials and methods
2.1 Study sites
2.1.1 Eddy covariance site (EUCFLUX)
The EUCFLUX site is located within a 200 ha plantation lo-
cated in south-eastern Brazil (São Paulo State; 22◦5800400 S
and 48◦4304000 W, 750 m a.s.l.) and is managed under a co-
operative project of the IPEF (Instituto de Pesquisas e Es-
tudos Florestais) (Nouvellon et al., 2019). The precipitation
was on average 1536mm yr−1(from 2008 to 2017), with
a drier season between June and September, and the mean
annual temperature was 19.3 ◦C. Soils are deep Ferralsols
(>15 m). A clonal plantation of a fast-growing Eucalyp-
tus grandis ×urophylla hybrid was established in Novem-
ber 2009 and harvested in June 2017. At the centre of the
stand, a flux tower continually measured meteorological vari-
ables as well as the fluxes of CO2and water vapour between
the plantation and the atmosphere, with the eddy covariance
method (Baldocchi, 2003). The study area was described in
detail in Christina et al. (2017), Nouvellon et al. (2010), Nou-
vellon et al. (2019), and Vezy et al. (2018). The stand was fer-
tilised in November 2019 with 3.0g m−2of K2O, 3.3 g m−2
of P2O5, 1.8 g m−2of N, 400 g m−2of dolomitic lime, and
trace elements; then at 3 months with 3.6 g m−2of K2O and
3.12 g m−2of N; at 10 months with 6.72 g m−2of K2O and
3.08 g m−2of N; and at 20 months of age with 15.12 g m−2
K2O. This amounted to a total of 23.60 gK m−2from fertil-
isation and resulted in non-limiting nutrient availability for
tree growth during a rotation cycle. This value was higher
than the typical 12 gK m−2added on average in commercial
plantations during a rotation cycle (Cornut et al., 2021).
2.1.2 Fertilisation experiments (Itatinga)
A 2 ha split-plot fertilisation trial (three blocks with three
fertilisation treatments per block) was installed at the
Itatinga experimental station (23◦0204900 S and 48◦3801700 W,
860 m a.s.l.; University of São Paulo–ESALQ). It is located
12 km next to the EUCFLUX site, under similar climate and
soil conditions. A fast-growing Eucalyptus grandis clone was
planted in June 2010, and the soil–tree relationships were
studied over the entire rotation of 6 years (from planting to
harvesting). The experimental design was described in detail
in Battie-Laclau et al. (2014b). Six treatments (three fertili-
sation regimes and two water supply regimes) were applied
in three blocks. In the present study, we focus on the +K and
oK treatments with the undisturbed rainfall regime, which
consisted of a non-limiting fertilisation +K (17.55 gK m−2
applied as KCl at planting, with 3.3 gP m−2and 200 g m−2
of dolomitic lime and trace elements as well as 12 gN m−2
at 3 months of age) and an oK omission treatment where the
same fertilisers as in the +K treatment were applied except
for the K fertiliser. The area of each individual plot in the
experiment was 864 m2.
The concentrations of different elements (N, P, K) in the
organs (leaves, trunks, branches, and roots) were measured
at an annual time step in eight individuals of each fertilisa-
tion treatment and upscaled to the whole stand using allomet-
ric relationships (not shown). Biomass and nutrient contents
were calculated (using upscaling) from inventories, biomass,
and nutrient concentration measurements conducted at 1, 2,
3, 4, 5, and 6 years in each fertilisation treatment. Atmo-
spheric deposition (0.55 gK m−2yr−1) and canopy leaching
fluxes (0.42 gK m−2yr−1) were measured in a nearby exper-
iment from Laclau et al. (2010).
The clones that were planted at the Eucflux and Itatinga
stands were different. This has an impact on the response
of the trees to environmental conditions, canopy function-
ing (Attia et al., 2019; Le Maire et al., 2019), and more im-
portantly stand GPP (Attia et al., 2019; Epron et al., 2012).
Distinct model parameter values were used for the more sen-
sitive parameters in the model, when differences were ob-
served in their measurements.
2.2 Complementary foliar measurements
Area, mass, and K-deficiency symptom development of indi-
vidual leaves were measured for the studied sites to param-
eterise the new leaf cohort sub-model and the K-deficiency-
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3096 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
symptom area sub-model described below. To this aim, we
used the scanned pictures (tabletop scanner device model
HP ScanJet G4050; 300 dpi) of leaves collected during the
biomass samplings at both sites (every 6 months at EU-
CFLUX and annually at Itatinga), on at least six trees per date
and treatment, and at three crown levels. Individual leaf areas
as well as the proportion of anthocyanic symptoms on indi-
vidual leaves were automatically computed from the images
based on a colour threshold calibrated by photointerpreta-
tion and automatised in a MATLAB®script (le Maire, 2023).
The leaf-scale metrics of each canopy third were upscaled to
stand averages using linear regressions with individual tree
D2H (i.e. the product of squared diameter with tree height).
Regressions were done using the scikit-learn Python library
(Pedregosa et al., 2011). The resulting parameters and func-
tions were then applied to the D2H of trees using inventories
of diameter and height of plots. This allowed the upscaling
of leaf individual area and symptomatic leaf area in order to
compute their plot averages.
2.3 CASTANEA-MAESPA general model presentation
The soil–vegetation–atmosphere carbon and water balance
were simulated with the CASTANEA-MAESPA model
for the EUCFLUX and Itatinga eucalypt plantations.
CASTANEA-MAESPA was the merging of the CASTANEA
model (Dufrêne et al., 2005) with the MAESPA model (Du-
ursma and Medlyn, 2012), the latter being modified as in
Christina et al. (2017). CASTANEA is an ecophysiological
model simulating the fluxes of carbon and water between
a forest stand (average tree) and the atmosphere at a half-
hourly time step. In its basic version, it includes no repre-
sentation of the hydraulic soil–plant–atmosphere continuum,
which is however critical in the context of a coupled carbon–
water–potassium model. The MAESPA model (Duursma
and Medlyn, 2012) was developed using the above-ground
components of the MAESTRA model (Wang and Jarvis,
1990) and the water balance components of the SPA model
(Williams et al., 1996). MAESPA is a three-dimensional
model of light interception, energy balance, photosynthesis,
and evapotranspiration. These fluxes are computed from pre-
scribed description of individual trees along time and at the
scale of small volumes of leaves within each tree crown. The
soil–plant–atmosphere water continuum is explicitly simu-
lated by MAESPA.
It was not possible to adapt the CASTANEA model,
initially developed on temperate Beech (Fagus sylvatica)
forests (Dufrêne et al., 2005), to the particular study case of
tropical eucalypt plantations, as we did previously for several
temperate and Mediterranean species (e.g. Delpierre et al.,
2012; Davi et al., 2006; Le Maire et al., 2005). Indeed, trop-
ical eucalypt plantations can grow roots down to a depth of
6 m the first year after planting (Christina et al., 2011), which
violates the CASTANEA assumption of a constant rooting
depth over the simulation period and the use of a simple
soil water bucket model. The MAESPA model does not have
this constraint and can easily be adapted to simulate an in-
creasing amount of extractable water (Christina et al., 2017).
Moreover, MAESPA had already been parameterised and ap-
plied at the EUCFLUX and Itatinga sites (Christina et al.,
2015, 2017). However, although it simulates fluxes of car-
bon and water, MAESPA is not a full carbon balance model,
in the sense that it does not simulate the carbon allocation
within the plant, litterfall, and soil organic matter decom-
position, etc. As such, contrary to CASTANEA, MAESPA
does not alone provide the structure required to simulate the
K balance. Therefore, the merging of both models into the
CASTANEA-MAESPA model aimed to offer a relevant and
extensive ecophysiological model for C and water cycles in
eucalypt plantations, prior to the implementation of the K
processes as described below.
The modules of CASTANEA simulating light intercep-
tion, water interception, carbon allocation and the growth of
organs, and organ respiration were coupled with the mod-
ules of MAESPA simulating soil water dynamics, leaf photo-
synthesis, transpiration, and plant hydraulics (Fig. S1). More
precisely, the coupled version includes the following points:
1. CASTANEA computes the diffuse and direct incoming
radiation reaching sun and shade leaves of a canopy
layer (25 canopy layers of varying surface).
2. This radiation is used in MAESPA to compute leaf-
scale carbon and water processes (half-hourly time
step), based on what is done usually at voxel scale in
MAESPA.
3. Net photosynthesis is calculated by MAESPA per
canopy layer and summed up at canopy scale (half-
hourly time step), then CASTANEA simulates the car-
bon allocation to the different organs, the organ respira-
tion, and their resulting growth (daily time step).
4. CASTANEA computes the rainfall interception and
throughfall, and therefore the water entering in the soil.
MAESPA continues the water cycle simulation with
water infiltration in the soil; evaporation; water uptake
from different soil layers (50 soil layers of 50cm) and
the water table; transpiration; water potential in the soil,
roots, and leaves; and impact of leaf water potential on
stomatal conductance
Note that the model description of all processes listed
above are described in the reference papers of Dufrêne et
al. (2005) for CASTANEA and Duursma et al. (2012) for
MAESPA (adapted to eucalypts in Christina et al., 2017 and
Vezy et al., 2018).
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3097
2.4 Model of eucalypt canopy dynamics
2.4.1 Overview of the leaf cohort model
Highly productive tropical eucalypt plantations in Brazil
grow from seedlings to 25–30 m high trees in the span of
6–7 years. The plantations present a continuous foliar phe-
nology with leaf production and leaf fall throughout the year.
This has previously led to the development of a canopy dy-
namics model (Sainte-Marie et al., 2014). While this model
was sufficient to explain leaf production and leaf fall dynam-
ics, we found it necessary to develop a new cohort-based
canopy dynamics model (summarised in Fig. 1), as there was
a need for the simulation of both K cycling in the canopy
and the effects of K on foliar ontogeny (Laclau et al., 2009;
Battie-Laclau et al., 2013). A daily time step was necessary
for the simulation of expansion and fall of the leaves of each
cohort. All leaves within a cohort were considered to have
the same physiological characteristics, growth, and lifespan.
A cohort was characterised by a number of leaves per square
metres of ground, individual leaf area, and mass. Leaf fall
occurred when leaves reached a certain K minimum thresh-
old or the end of their lifespan. This new leaf cohort model
is described in the next sections, in the case of no limitation
by K.
2.4.2 Leaf cohort production
A new cohort was initialised daily. The number of leaves
Nproduced in the cohort was a function of the height in-
crease of the trees. Indeed, in these fast-growing plantations,
most of the new leaves are produced in the top-most part of
the crown. The increase in tree height can be computed in
the CASTANEA-MAESPA model as the result of increase in
trunk biomass and with allometric parameters relating stand
biomass and stand height (see the following companion pa-
per: Cornut et al., 2022).
The relationship between daily height increase and leaf
production was corrected by a flattening factor. This means
that even if the daily height increase was close to zero or even
null, leaf production would still happen at a slower but pos-
itive rate. The model generated a number of new leaves per
m2at a daily time step following this function:
N=1H +fp
1+fp
×κ, (1)
where Nwas the daily number of leaves produced in num-
ber of leaves per metre squared of ground, and 1H (m) was
the increase in tree height. fpwas the flattening factor, mean-
ing that if fp=0, then leaf production was linearly related to
height increase, and as fpincreased, Ntended towards a con-
stant function. κ(nleaves m−2
ground m−1
height) is a conversion fac-
tor from height increment to number of new leaves. The pa-
rameters used here were fitted using experimental data from
the fully fertilised stand. The calibration was a systematic
exploration of parameter space using multiple normalised
RMSE (addition of the normalised RMSE for multiple vari-
ables; see Eq. S1) as a goodness-of-fit indicator. The data
used for calibration were destructive leaf biomasses (eight
trees and upscaling using a stand inventory at a yearly time
step over the rotation), leaf area (same as leaf biomass), and
leaf fall (12 L traps at a monthly time step over the rota-
tion) measurements. The calibration was done on cumulative
leaf production and leaf fall to maintain consistency in the
long-term carbon fluxes rather than focusing on their instan-
taneous changes.
2.4.3 Leaf cohort lifespan
As long as K was not limiting, the lifespan of a cohort was
considered to be constant, since the leaf lifespan deduced
from leaf biomass and leaf fall measurements in fully fer-
tilised stand did not show major trends along the rotation,
and the amplitude of seasonal changes in lifespan was lim-
ited (Fig. S4e). Since no mechanistic explanation was avail-
able, we refrained from implementing it in the model. For
the sake of simplicity, we did not consider in the present
simulations the fall of leaves resulting from extreme events
(drought, frost, or heatwave). Indeed, in the studied sites, no
large leaf fall due to extreme events was observed. Hence, the
leaf lifespan (days), LLS, in non-limiting K conditions was
fixed to the average measured value of 480. This average leaf
lifespan was estimated as the ratio of the measured annual
average leaf biomass (measured annually on eight trees and
upscaled using whole-stand inventories) and the annual sum
of litterfall (measured monthly).
2.4.4 Leaf expansion in area in the cohort
For a given cohort, individual leaf area (LA) expands from a
virtually null area at initialisation of the cohort up to an area
of LAmax (mm2). The leaf area dynamics followed a sigmoid
function (Fig. 2a; Battie-Laclau et al., 2013). Leaf area was a
function of time and not thermal time (as for instance in the
original CASTANEA model), since no calibration data were
available and it was not deemed necessary for this model.
Therefore, the daily leaf area expansion was forced to follow
the sigmoid derivative function as
1LA
1t =kLA ×LAmax ×e−kLA(t−t50LA )
e−kLA(t−t50LA )+12,(2)
where 1LA
1t (mm2d−1) was the daily growth in the area of
an individual leaf within a given cohort; t(days) was the
number of days since leaf cohort creation; LAmax (mm2) was
the (non-limited) maximum leaf area; kLA (d−1) was a slope
parameter; and t50LA (days) was the inflexion point of the
original sigmoid of leaf area increase, meaning that it was
the date on which leaves increased the most and on which
the leaf area (LA) reached half of the maximum leaf area
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3098 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
(LAmax). The parameters LAmax,kLA, and t50LA were fit-
ted from 70 measured expanding leaves (Battie-Laclau et al.,
2013) in non-limited fertilisation conditions using RMSE as
a goodness-of-fit indicator. Parameters kLA and t50LA were
assumed not to vary along the stand rotation. LAmax was also
assumed to be constant, since the leaf scans did not show
any explainable trends of mean leaf area during the rotation
(Fig. S5).
The total leaf area of a given cohort was given by the prod-
uct of LA, the area of an individual leaf, and N, the number
of leaves in the cohort. The total leaf area of the stand at a
given date was calculated by adding up all the cohort areas.
2.4.5 Leaf expansion in mass in the cohort
Individual leaf mass increase within a cohort was similar in
shape to the leaf area increase but with a temporal shift, since
leaf mass per area continues to increase when the maximum
leaf area is attained as follows:
1BF
1t =kBF ×BFmax ×e−kBF(t−t50BF )
e−kBF(t−t50BF )+12,(3)
where 1BF
1t (g d−1) was the daily growth in mass of an indi-
vidual leaf in a given cohort, t(days) was the number of days
since leaf cohort creation, BFmax (g) was the maximum indi-
vidual leaf mass, kBF (d−1) was a slope parameter, and t50BF
(days) was the inflexion point of the original sigmoid of leaf
mass increase; therefore it was the date of maximum leaf area
increase and also the date when half BFmax was reached. The
parameters kBF and t50BF were calibrated using individual
leaf biomass data and results from Laclau et al. (2009).
Specific leaf area (SLA) of individual leaves showed a
decreasing relationship with tree height (Fig. S6a), while
LAmax was more constant as described before (Fig. S5). We
thus assumed that BFmax increased with tree height:
BFmax =minBFrotation
max ,sBF ×HP×TC,(4)
where BFmax (gC) was the maximal mass of an individual
leaf of a cohort at the end of leaf expansion in mass, BFrotation
max
(gDM) was the maximum mass of an individual leaf through-
out the rotation, sBF and Pwere the parameters of the power
function between leaf mass and tree height H(m), and TC
(gC gDM−1) was the leaf carbon content.
2.4.6 Leaf water content
In non-limited nutrient conditions, leaf cell expansion in area
was associated with a leaf water inflow in order to maintain
an optimum leaf turgor. This water inflow was computed as
Wxylem→leaf =0×1S
1t ,(5)
where Wxylem→leaf (mL d−1) was the water inflow into the
expanding leaf (this was “structural” water associated to the
creation of new tissues, not to be confounded with the wa-
ter used for leaf transpiration), Sthe leaf area of the cohort
(mm2), computed in Eq. (2), and 0(mL mm−2) was the sur-
facic water content, i.e. the amount of leaf water per leaf area
at full turgor. 0was assumed to be a constant.
Experimental data have shown that at the end of leaf area
expansion, when the leaf has reached its maximum area,
there was some water outflow, defined hereafter as water ex-
pulsion. This is an assumption made from observations of a
slight decrease in K leaf content following the end of leaf
expansion (Laclau et al., 2009). This leaf water (containing
ions) expulsion, probably corresponding to a loss of cell wall
extensibility (Pantin et al., 2012) during the maturation of
leaf tissue, was limited in quantity and in duration. Hence,
the overall leaf water content dynamic starts increasing until
a maximum at the end of the leaf area expansion, followed by
a small decrease until a constant plateau. This plateau corre-
sponds to the water content necessary to maintain a constant
leaf turgor in optimal conditions. The water expulsion flux
was computed as
Wleaf→phloem = −minα× 1−Wleaf
Wturgor
leaf !,0,(6)
where Wleaf→phloem (mL d−1) was the flux of water leaving
the leaf at the end of leaf expansion, α(mL d−1) was the
constant rate of water expulsion fitted using fine-scaled leaf
K concentrations (Laclau et al., 2009), Wleaf (mL) was the
amount of water in an individual leaf on the previous day,
and Wturgor
leaf (mL) was the amount of water found in the leaf
at the final plateau. Wturgor
leaf was computed as 0×LAmax.
Finally, the variation of leaf water content for an individual
leaf in a cohort (Wleaf; mL) was computed by adding the daily
net flow 1Wleaf
1t given by
1Wleaf
1t =Wxylem→leaf −Wleaf→phloem.(7)
2.5 Ecosystem model of the K cycle
We now introduce the CASTANEA-MAESPA-K model, which
simulates K cycling in the plantation, and its interactions
with the ecosystem carbon and water cycles (Fig. 1). K re-
mains in its ionic (K+) form throughout the ecosystem cy-
cle (Marschner, 2011). Modelling the circulation of K within
the plants as well as between the plant and the soil was
deemed necessary, since K+cations show great mobility in
the ecosystem (Marschner, 2011). Similarly to the leaf co-
hort model, a daily time step was used for the K-cycle sub-
model. The K cycle was modelled using seven explicit K
pools (Fig. 1): soil K (subdivided in the fractions of soil
K available and not available for root uptake), soil K fer-
tiliser added (the fertiliser before dissolution), litter K, xylem
sap K, phloem sap K, leaf K, and other plant organs K (see
the following companion paper: Cornut et al., 2022). These
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3099
K pools were connected by fluxes (root uptake, resorption,
and leaching, etc.), and K inputs (fertilisation, atmospheric
deposition, and rock weathering) entered this open system
(Fig. 1).
K entered into the soil through fertiliser inputs, atmo-
spheric deposition, and rock weathering. After uptake by
roots, K circulated throughout the plant through the xylem
sap and the phloem sap, which provided the K necessary to
the leaves and organs (Cornut et al., 2022) as well as the K
needed for phloem functioning. Part of the K in the phloem
was recirculated back into the xylem and thus created a feed-
back for K uptake by roots. Indeed, soil K uptake by roots
depends on the gradient between soil and xylem K. Leaves
contribute to the cycle through resorption, canopy leaching,
and litterfall. The flux of K from branch, bark, and fine root
to litter was simulated but is not described here (see Cornut
et al., 2022). The K in the litter was leached following a rate
that depended on throughfall precipitation amount. It then
entered the soil, to be once again available for uptake. There
was no simulated biologically mediated K release from the
litter, since no reference to this process was found in the lit-
erature. Moreover, measures of K concentration in the litter
of leaves, branches, and bark all decreased exponentially at
the same rate (Maquère, 2008). This was not the case for N
and P (known for their biologically mediated release), indi-
cating that K release from the litter is indeed mainly the result
of leaching. The only outgoing flux from the system is the
amount of K lost by deep leaching and the trunk K exported
from the stand at harvest. Deep leaching was not simulated
here, since there was no evidence of any losses by deep leach-
ing at these sites owing to the soils’ cationic exchange capac-
ity and depth (Maquère, 2008; Caldeira Filho et al., 2023). K
was accumulated in organs (trunk, branches, roots), but this
allocation sub-model will be presented in the companion pa-
per (Cornut et al., 2023). This K cycle allowed us to create a
feedback between K availability and GPP through the effect
it has on leaf expansion, leaf lifespan, and photosynthetic pa-
rameters (see below).
2.5.1 Soil K
Soil K content (Ksoil; gK m−2) was initialised in the model at
the tree-planting date (EUCFLUX: 7 October 2009, Itatinga:
1 June 2010) with a measured value Kt0
soil, calculated using K
concentration in soil, and soil bulk density at different depths
(Maquère, 2008). Then, this value was updated daily with
incoming and outgoing fluxes.
The K that is added daily to the K litter pool (Klitter) is
the K reaching to the ground through leaf fall (Eq. 27), bark
fall (Cornut et al., 2023), branch fall (Cornut et al., 2023),
and entering the soil litter pool through fine root turnover
(Cornut et al., 2023). Instead of a fixed decomposition rate
of K in litter, the model considered K release from litter to be
mainly coming from leaching with water, since K is a cation
that is not strongly adsorbed on organic surfaces. Litter K re-
lease measurements done at the experimental site (Maquère,
2008) showed very similar K release rates for branches, bark,
and leaves, further confirming this hypothesis. Moreover, K
is released faster than either C, N, or P contained in the litter,
suggesting a leaching process independent of litter decompo-
sition. Since we assumed the leaching rate was independent
of the litter type, all simulated K litter has been pooled into a
unique K litter compartment (Klitter). The following equation
was used for K leaching from the litter to the soil:
Klitter→soil =σ×Pground ×Klitter,(8)
where Klitter→soil (gK m−2d−1) was the litter K leaching
flux, Pground (mm d−1) was the daily amount of precipitation
reaching the ground, σ(mm−1) was the conversion factor be-
tween the K litter leaching rate and throughfall precipitation,
and Klitter (gK m−2) was the amount of K in the litter. σwas
estimated on annual data by dividing the measured K leach-
ing rate (Maquère, 2008) by the annual precipitation that falls
on the ground (throughfall).
K fertilisation was applied at the beginning of the rotation
at several dates, in a solid form (crystals of KCl), and located
close to the Eucalyptus plants. The flux of K from this solid
fertiliser compartment (Kfertiliser; gK m−2) to the soil K com-
partment was simulated using the following equation:
Kfertiliser→soil =sfertiliser ×Kfertiliser,(9)
where Kfertiliser→soil (gK m−2d−1) was the flux of K from
the fertiliser compartment to the accessible soil K pool, and
sfertiliser was the decomposition rate of K fertiliser in d−1.
Observations in the fields showed that the KCl fertiliser
dissolved quickly at EUCFLUX and Itatinga (less than 2
months).
Atmospheric K deposition is modelled as a constant flux.
We used the values measured at Itatinga (Laclau et al.,
2010). They amounted to a mean input of Katmosphere→soil of
0.55 gK m−2yr−1distributed uniformly throughout the year.
This amount feeds directly into the total Ksoil pool.
Deep soil K leaching was included in the model but was
parameterised to be a null flux, as was measured in the plan-
tations under study (Maquère, 2008). The K entrance to the
soil pool from mineral weathering was simulated as a con-
stant flux. K flux from weathering is directly added to the ac-
cessible soil, since this process mainly takes place in the rhi-
zosphere (Pradier et al., 2017). However, as for deep leach-
ing, there is no clear evidence of this flux in the soils under
study, where values between 0 and 0.3 gK m−2yr−1are given
(Cornut et al., 2021): we therefore also set this flux to zero.
Only a portion of Ksoil was accessible to the roots at the
beginning of the rotation because of the time spent for root
horizontal and vertical expansion. Because K was mainly lo-
cated in the top soil layers (Maquère, 2008), and because root
growth in depth was very fast (Christina et al., 2011), only
the horizontal root exploration was considered in the model.
An empirical relationship between tree height and area root
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3100 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
Figure 1. Schematic representation of the soil and plant components of the K cycle, and their links with the leaf cohort model and other
sub-models. On the left is a schematic representation of the canopy leaf cohort sub-model. Black arrows represent a functional link a variable
has with another variable or process. Dashed lines represent an influence of one process (black), pool (purple), or state (light purple) over
a process or pool. On the right a schematic representation of the K flux and pool sub-model. Purple boxes are K state variables, and purple
arrows are K fluxes. K fluxes simulated with a simple Ohm’s law form are represented with resistance symbols. The numbers in exponential
form correspond to the numbers of the equation in the text. The K pools of other organs (woody and roots) and their link to the K circulation
model are semi-transparent, since they are described in the companion paper (Cornut et al., 2023).
radius around individual trees was described in Gonçalves
(2000) as follows:
rootradius =0.80 ×H−0.075,(10)
where rootradius (m) was the average radius of the horizontal
root front around a tree, and H(m) was the tree height (Cor-
nut et al., 2023). Since the planting density was 1666 trees
per hectare, a full exploration of the soil was obtained when
tree had explored a circle of 6 m2area:
Kaccessible
soil =(rootradius)2×π
6×Ksoil,(11)
where Kaccessible
soil (gK m−2) was the soil K accessible for plant
uptake, and Ksoil (gK m−2) was the total bioavailable soil K.
The fraction is the ratio of root accessible soil to total soil,
bounded between 0 and 1.
Because of the root exploration dynamics, the initial K in
the system Kt0
soil was progressively available to roots, at a
proportion following the increase in the root explored area.
Following the same logic, the amount of K coming from the
litter decomposition and atmospheric deposition entered the
total soil K pool Ksoil, but only a part of this Ksoil was avail-
able for plant uptake (called Kaccessible
soil ). However, the three
other incoming fluxes of K to the soil were considered to be
directly accessible for root uptake (i.e. they enter directly in
the Kaccessible
soil pool) as follows: (1) the fertiliser flux, since
fertilisers are applied close to trees at planting or when the
root system is exploring the whole volume of the upper soil
layers for other fertiliser applications, (2) the K flow coming
from soil weathering because most of the weathering takes
place in the rhizosphere (Pradier et al., 2017; de Oliveira
et al., 2021), and (3) the canopy leaching flux because it en-
ters the soil mostly below the crown foliage. K foliar leach-
ing (Kleaves→soil) was computed within the leaf K sub-model,
described below (Eq. 28).
2.5.2 Uptake of soil K and cycling in xylem and phloem
To calculate the K uptake by trees in the soil and the fluxes
of K in the plant, it was necessary to calculate the optimal
quantity of K in the phloem sap. Furthermore, K in phloem
sap is essential to a wide range of processes (e.g. loading
and unloading of sugars) (Cornut et al., 2023). For these pro-
cesses, the plant maintains a fairly constant K phloem sap
concentration [K]phloem. To compute this K quantity in the
phloem, values of optimal K concentration in the phloem
sap ([K]opti
phloem), minimum K concentration in the phloem sap
([K]min
phloem), and phloem sap volume (Vphloem) per unit sur-
face were needed.
[K]opti
phloem was considered to be the maximum concentra-
tion of K in the phloem sap measured in the fully fertilised
stand (Battie-Laclau et al., 2014b). [K]min
phloem was assumed to
be the minimum concentration of K in the phloem sap mea-
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3101
sured in the K omission stand of the same experiment (Battie-
Laclau et al., 2014b).
Estimating Vphloem was done through relationships be-
tween phloem sap volume and xylem sap volume, since no
direct measurements or estimates were available. Xylem sap
volume was considered to be a function of basal area, sap-
wood area at DBH (Guillemot et al., 2021), height of the tree,
and branch and root biomasses. The trunk cross section was
divided into sapwood area and heartwood area. The trunk (re-
spectively heartwood) volume was modelled as a cone with a
base disc of area equal to the basal area (respectively equal to
the heartwood area). Trunk sapwood volume was estimated
as the difference between trunk volume and heartwood vol-
ume. Branch and root sapwood volume were deduced from
their biomass, considering that branches and root biomass are
entirely composed of sapwood. Their volume were computed
using the density of eucalypt sapwood. The lumen volume
of the xylem (i.e. the xylem sap volume) was considered to
be 13.6 % of total xylem volume as reported in general for
angiosperms (Zanne et al., 2010), since no eucalypt-specific
data were available. Following Hölttä et al. (2013), and con-
sidering the relatively similar lumen proportion between both
xylem and phloem (Nobel, 2005), phloem sap volume was
considered to be 2 % of the total xylem sap volume.
Uptake of K from the soil by the trees was a function of de-
mand by growing organs, remobilisation of K from senescent
organs, and soil supply. The amount of K available for uptake
was computed in Eq. (11). K demand by the trees needs to be
calculated. To that end, the following was calculated.
First, the target amount of K in the phloem was calculated
as
Ktar
phloem = [K]opti
phloem ×Vphloem +KNPP +Kdemand
leaf ,(12)
where Ktar
phloem was the target amount of K in the phloem sap
(gK m−2), [K]opti
phloem was the optimal K concentration in the
phloem sap (gK L−1), Vphloem was the volume of phloem sap
(dm 3m−2), KNPP was the optimal quantity of K needed for
organ growth, and Kdemand
leaf was the optimal quantity of K
needed for leaf development.
Finally the demand for K uptake from the soil is the fol-
lowing:
Kdemand
soil→xylem =
Ktar
phloem +Ktar
xylem
−Kphloem +Kremob +Kxylem
1t ,(13)
where Kdemand
soil→xylem (gK m−2d−1) was the quantity of K up-
take necessary for optimal tree functioning, Ktar
phloem was
from Eq. 12, Ktar
xylem (gK m−2) was the target amount of K
in the xylem sap, Kphloem (gK m−2) was the amount of K in
the phloem sap, Kremob (gK m−2) was the amount of K re-
mobilised from the woody organs (Cornut et al., 2023), and
Kxylem (gK m−2) was the amount of K in the xylem.
Uptake of K from the soil to the xylem sap is the minimum
between the soil “offer”, i.e. what can be taken up from the
soil knowing the soil K content and the soil-to-root K resis-
tance, and the xylem K “demand”:
Ksoil→xylem =minKaccessible
soil
Rsoil→xylem ,Kdemand
soil→xylem,(14)
where Ksoil→xylem (gK m−2d−1) was the uptake flux, Ksoil
(gK m−2) was the amount of K in the accessible soil,
Rsoil→xylem (days) was the resistance to absorption by plant
roots, and Kdemand
soil→xylem (gK m−2d−1) was the uptake demand
from Eq. (13).
In the model, internal K cycling (Marschner et al., 1996)
was a necessary process that provides feedback for the up-
take of K from the soil, maintaining K homeostasis in the
phloem sap, and linking organ remobilisation and allocation
of K for growth. In the K circulation model (Fig. 1), two K
fluxes are represented, one from the phloem sap to the xylem
sap (representing a flux mainly happening in roots in plants)
and one from xylem sap to phloem sap (mainly happening
in the shoots). These representations allowed the phloem sap
to maintain a K content of phloem close to optimal values
(Eq. 12).
Firstly, the flux of K from the xylem sap to the phloem sap
was calculated. It was a function of phloem “demand” and
xylem sap K of the previous time step. We assumed that all
the K available in the xylem sap could potentially be trans-
ferred to the phloem sap the next day as follows:
Kxylem→phloem =minmaxKtar
phloem −Kphloem
1t ,0
Kxylem
1t ,(15)
where Kxylem→phloem (gK m−2d−1) was the flux of K from
the xylem to the phloem, Kxylem (gK m−2) was the amount
of K in the xylem sap, Kxylem (gK m−2) was the amount of
K in the phloem sap, and Ktar
phloem was from Eq. (12).
The transport of K from the phloem to the xylem took
place if K concentration in the phloem sap was higher than
its optimal value (e.g. following leaf resorption) as follows:
Kphloem→xylem =maxKphloem −Ktar
phloem
1t ,0,(16)
where Kphloem→xylem (gK m−2d−1) was the flux of K from
the phloem to the xylem, and Ktar
phloem was from Eq. (12).
2.5.3 K cycling in the leaves
The leaf K balance equation of the individual leaf of each
leaf cohort was given by the following sum of fluxes:
1Kleaf
1t =Kphloem→leaf −Kleaf→soil −Kleaf→phloem
−Kleaf→litter,(17)
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3102 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
where 1Kleaf
1t (gK d−1) was the daily variation of the quantity
of K in an individual leaf of a given cohort; Kphloem→leaf was
the amount of K entering the leaf during leaf expansion (see
Eq. 22); Kleaf→soil was the canopy leaching flux (see Eq. 28);
Kleaf→phloem was the sum of K following water expulsion at
the end of leaf expansion (Eq. 24), the maximum between
K resorption driven by the phloem demand (Eq. 25), and the
K resorption at leaf senescence (Eq. 26); and Kleaf→litter was
the K flux occurring the last day of the cohort, when the leaf
was simulated to fall. Leaf K inflow (Kphloem→leaf) was com-
puted as a function of the K offer by the phloem and K de-
mand for leaf growth at the canopy scale and organ growth
at the tree scale.
The calculation of the water inflow in the leaf during leaf
expansion was calculated first in the case of no K limita-
tion (Wxylem→leaf in Eq. 5). This allowed the calculation
of a theoretical optimal K flux entering the expanding leaf,
Knonlimited
phloem→leaf, computed considering an optimal concentra-
tion of K in the water entering the leaf, [K]max
leaf (gK mL−1).
This value was approximated as the maximum concentration
found in the leaf water on different measurement campaigns
(Battie-Laclau et al., 2013; Laclau et al., 2009). The resulting
K flux was the non-limited rate of K entrance in the expand-
ing leaf:
Knonlimited
phloem→leaf = [K]max
leaf ×Wxylem→leaf,(18)
where Knonlimited
phloem→leaf (gK d−1) was the maximum entrance of
K+ions in the expanding leaf.
However, restriction of this flux occurs due to the phloem
limitation of K supply at canopy scale that may not attain
the K demand for optimal growth. A reduction of the K in-
flow in the leaf was therefore applied if the leaf demand at
canopy scale Kdemand
leaf was higher than the available Kphloem
(the “offer”).
Kdemand
leaf (gK m−2) was the K demand of all expand-
ing leaves of the stand and was computed as the sum of
Knonlimited
phloem→leaf ×Nfor all leaf cohorts (with Nthe number of
leaves of each cohort; see Eq. 1) as follows:
Kdemand
leaf =
t
X
i=1Knonlimited
phloem→leafi×Ni.(19)
To calculate the phloem sap “offer”, the following rela-
tionship was used:
Kphloem→organs =minKphloem − [K]min
phloem ×Vphloem,
KNPP +Kdemand
leaf ,(20)
where Kphloem→organs (gK m−2) was the amount of K avail-
able for leaf expansion and organ growth in the phloem sap,
Kphloem (gK m−2) was the total amount of K in the phloem
sap, [K]min
phloem (gK L−1) was the minimal concentration of
K in the phloem sap, Vphloem (L) was the phloem sap vol-
ume, KNPP (gK m−2) was the optimal amount of K for organ
growth (Cornut et al., 2023), and Kdemand
leaf (gK m−2) was the
demand for optimal leaf expansion.
Then the limitation of K for leaf expansion was calculated
as a ratio of available (“offer”) K-to-K demand:
LK=
Kavailable
phloem
KNPP +Kdemand
leaf
,(21)
where LKwas the ratio of available K in the phloem sap
to demand of K from organ growth and leaf expansion,
Kphloem→organs (gK m−2) was available phloem K (Eq. 20),
and KNPP and Kdemand
leaf were organ growth and leaf expansion
demands respectively (both gKm−2; see above).
The quantity of K entering the expanding leaf was thus
defined as the following:
Kphloem→leaf =Knonlimited
phloem→leaf ×LK,(22)
where Kphloem→leaf (gK d−1) was the amount of K+ions
that enter the expanding leaf in limited K conditions,
Knonlimited
phloem→leaf was computed in Eq. (18), and LKwas com-
puted in Eq. (21).
The K outgoing flux from leaf to phloem (Fig. 2b) can be
decomposed into
Kleaves→phloem =Kexpulsion +maxKphloem
resorption, K senescence
resorption .(23)
where Kexpulsion (gK m−2d−1) was the K flux leaving the leaf
during leaf maturation (Eq. 24), Kphloem
resorption (gK m−2d−1) was
the resorption flux driven by phloem sap demand (Eq. 25),
and Ksenescence
resorption (gK m−2d−1) was the resorption flux driven
by leaf senescence (Eq. 26).
Kexpulsion =Wleaf→phloem ×Kleaf
Wleaf (24)
Here, Wleaf→phloem was calculated in Eq. (6); Wleaf was the
previous day’s leaf water content, calculated in Eq. (7); and
Kleaf was the previous day’s leaf K content of the cohort.
The K resorption flux Kresorption from the leaf to the
phloem could be activated by low phloem K content. This
was a mechanism to maintain homeostasis in the phloem,
since K was essential for many phloem functions (Cornut
et al., 2021). Evidence was also provided by leaves losing K
during their lifespan, especially in K-deficient trees (Battie-
Laclau et al., 2013). Another piece of evidence was the high
concentrations of K in the petiole compared to other leaf
parts (Fig. S9d). This was not the case for N (Fig. S9c) and
suggests an intense circulation of K to and from the leaf. The
resorption of the leaf towards the phloem was
Kphloem
resorption =Kleaf
Rleaf→phloem
×(1−LK), (25)
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3103
where Kphloem
resorption (gK d−1) was the cohort phloem-driven re-
sorption, Kleaf (gK) was the K content of leaves in the cohort,
Rleaf→phloem (days) was the resistance to resorption, and LK
was the K limitation computed in Eq. (21).
The leaf K resorption flux during leaf senescence
Ksenescence
resorption followed a sigmoid function:
Ksenescence
resorption =e−kr(t−LLS)
e−kr(t−LLS)+12,(26)
where Ksenescence
resorption (gK d−1) was the resorption flux occurring
at leaf senescence, just before leaf fall. LLS (days) was the
leaf lifespan, which was also the inflexion point of the sig-
moid, and krwas the parameter corresponding to the speed
of the resorption flux at the inflexion point. We approximated
the time it took for active K resorption to be 1w, as K+ions
are highly mobile, and evidence from chlorophyll degrada-
tion at senescence suggests extremely fast dynamics (Mattila
et al., 2018).
The K flux from leaves to litter was the sum of each falling
cohort multiplied by the K content of the respective leaf co-
hort at leaf fall:
Kleaves→litter =
n
X
0Kfall
leafi
,(27)
where Kleaves→litter (gK m−2d−1) was the K flux from
leaves to litter, nwas the total number of falling leaf cohorts,
iwas the number of each individual falling leaf cohort, and
Kfall
leaf (gK m−2d−1) was the amount of K from each cohort
that fell and reached the K litter pool.
We assumed that the daily canopy leaching flux strength
was proportional to the throughfall that occurs during precip-
itation as observed previously in a eucalypt forest (Crockford
et al., 1996):
Kleaves→soil =λ×Wtip ×Kleaf,(28)
where λ(mm−1
throughfall) was the fraction of leaf K that was
leached per millimetre of daily throughfall, Wtip (mm) was
the throughfall, and Kleaf (gK) was the amount of K in the
leaf. λwas calibrated considering the leaf area index and leaf
K content of a well fertilised canopy as well as canopy K
leaching measurements (Laclau et al., 2010).
Finally, the K flux accompanying the leaf fall, Kleaf→litter,
happened following one of the two conditions: when leaf co-
hort lifespan LLS was reached, or when the K concentra-
tion in leaf water (Kleaf
Wleaf ) was below a threshold value [K]min
of 9.25e−5gK mL−1. At one of these dates, the leaf co-
hort was shed and Kleaf→litter =Kleaf. This [K]min threshold
value was either reached after resorption during senescence
or through other processes (phloem demand, Eq. 25; leach-
ing, Eq. 28) thus diminishing the leaf lifespan in K-deficient
trees. Indeed, leaf fall was related to strong K deficiency
in several studies (Laclau et al., 2009; Battie-Laclau et al.,
2013).
2.6 Impact of K limitation on the cohort growth model
2.6.1 Number of leaves produced at cohort
initialisation
Since leaf production was a function of tree height which it-
self is a function of tree trunk biomass, K availability could
have an indirect impact on leaf production through its impact
on tree trunk production. Briefly, tree trunk production could
be affected by a reduced allocation of C due to either a de-
crease in GPP or an increase in the share of C partitioned to
other organs (for more details on trunk production, see Cor-
nut et al., 2023). No specific impact of K deficiency on the
number of new leaves generated was included in the model,
since experiments have shown that leaf generation speed at
the branch level is not impacted by K availability, and leaf
biomass production is not substantially different between oK
and fully K fertilised stands (Cornut et al., 2021).
2.6.2 Impact of K limitation on individual leaf area
When there was no K limitation, in optimal conditions, leaf
expansion in area was computed as in Eq. (2), and the water
inflow was simply simulated to follow this leaf expansion as
in Eq. (5). However, under K limitation, individual leaf area
was strongly affected by K availability (Battie-Laclau et al.,
2013). Mechanistically, the increase of leaf area was driven
by a water flux entering the leaf, because the turgor pressure
participates to the cell expansion, following the logic of the
Lockhart model (Lockhart, 1965). The Lockhart model was
simplified in the present study due to the important number of
parameters of the original model that had not been measured
in our context and the difficulty regarding their calibration.
This model allowed to relate the K availability in the phloem
sap and the expansion of leaves at the individual leaf level on
a daily time step. Using the dynamic water content of leaves
during expansion, K demand for the cohort at each time step
was calculated. The availability of K in the phloem sap then
determined a K-limited water flux and thus the leaf expansion
rate (Fig. 2d).
First, K availability controls the water entrance flux
(Wxylem→leaf; Eq. 5) in the leaf during leaf expansion, since
there was a lower limit of osmotic potential required for the
entrance of water in the leaf cells.
WKlimited
xylem→leaf =Wxylem→leaf ×max Kphloem→leaf
Knonlimited
phloem→leaf
,r!(29)
Here, WKlimited
xylem→leaf (mL d−1) was the flux of water enter-
ing the leaf during leaf expansion reduced with K limita-
tion, Kphloem→leaf was from Eq. (22), Knonlimited
phloem→leaf was from
Eq. (18), and rwas a parameter r∈ [0,1]of the same order
of magnitude as the ratio of K-limited individual leaf area
compared to non-limited leaf area.
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3104 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
Secondly, leaf water content Wleaf was recalculated using
an updated value for the expansion (WKlimited
xylem→leaf instead of
Wxylem→leaf).
Finally, the non-limited leaf area expansion increment 1S
1t
computed in Eq. (2) was updated with a new K-limited leaf
area expansion increment1SKlimited
1t , considered to be directly
proportional to the water flux entering the leaf:
1SKlimited
1t =WKlimited
xylem→leaf ×1
0,(30)
where 1SKlimited
1t (mm2d−1) was the area increase of the ex-
panding leaf computed after accounting for K limitation,
WKlimited
xylem→leaf was obtained from Eq. (29), and 0(mL mm−2)
was the leaf surfacic water content.
2.7 Leaf K-deficiency symptoms and implication for
leaf photosynthesis
2.7.1 Leaf K-deficiency symptoms
When leaves experience strong K deficit, they display antho-
cyanic symptoms (i.e. they turn purple from the leaf mar-
gins; Gonçalves, 2000). This has a strong impact on the pho-
tosynthetic capacity of affected areas (Battie-Laclau et al.,
2014a). We assumed that leaf K-deficiency symptom area
results from the history of K deficiency the leaf has expe-
rienced since the beginning of its growth. This was modelled
as function of the accumulation of K deficit in the leaves over
time, called “deficit days” (DDs). The daily increase in DD
was computed as
1DD
1t =max([Kleaf]max ×Wleaf)−Kleaf,0,(31)
where 1DD
1t (g) was the daily increase of the deficit days,
[Kleaf]max (gK mL−1) was the optimal (maximal) foliar con-
centration of K, Wleaf (mL) was the amount of water in the
individual leaf (after K limitation; Eq. 7), and Kleaf (gK) was
the leaf K content.
The proportion of symptoms in a leaf (Fig. 2b, d) was then
computed as
SP =minDD ×2, SPmax,(32)
where SP was the leaf surfacic symptom proportion, DD was
the accumulated deficit days computed in Eq. (31), 2was a
conversion factor from deficit days to symptom proportion,
and SPmax was the maximum proportion of symptom area on
a single leaf, with 0 <SP <SPmax.
2.7.2 Impact of symptoms on leaf photosynthesis
Leaves, even with symptoms, continue to intercept radia-
tions. In the model, it means that the light interception sub-
model was not affected by symptom area; i.e. the total leaf
area of each cohort was not affected by leaf K symptoms.
Note that the total leaf area under K deficiency was reduced
through various processes such as lower number of produced
leaves because of lower growth in height (Eq. 1), reduction of
individual leaf sizes (Eq. 30), and through the shorter lifes-
pan of leaves because of K-deficiency-associated leaf fall
(Sect. 2.5.3).
However, leaf symptoms have a strong effect on leaf-scale
photosynthesis. Indeed, experimental results (Battie-Laclau
et al., 2014a) have demonstrated that the leaf-scale photo-
synthesis was strongly reduced when there was K-deficiency
symptoms. This decrease was almost linear, suggesting that
we could model leaf photosynthesis as fully active in the non-
symptomatic areas of the leaves and null in the symptomatic
area; i.e. the photosynthesis was reduced by the proportion
of symptoms in the leaf.
For the sake of simplicity, this was implemented in the
model by reducing the two leaf-scale photosynthetic param-
eters V cmax and Jmax according to the leaf area proportion
affected by symptoms as follows:
V clim
max =V cmax ×(1−SP), (33)
Jlim
max =Jmax ×(1−SP), (34)
where V cmax and Jmax were respectively the maximum car-
boxylation rate and the maximum rate of electron transport,
and SP was described in Eq. (32).
2.8 Model parameterisation and initialisation
The photosynthetic, stomatal, and soil parameters of the
model were obtained from Christina et al. (2017) and were
measured at the EUCFLUX site. The parameters of the new
cohort model and of the new K-cycle model were mostly
measured at the Itatinga site either during the rotation sim-
ulated here (Battie-Laclau et al., 2014b) or the previous K-
omission (Laclau et al., 2009) experiment at the same site.
The parameterisation was described along the equation de-
scriptions of Sect. 2.4 to 2.7 and reported in Tables S1, S2,
and S3. The calibration of the simulated processes was only
done in the +K condition, since the responses of different
processes to K deficiency were derived from measured or
estimated parameters (except for the leaf expansion process
which was calibrated in both +K and oK conditions using
Battie-Laclau et al., 2013; see Tables S1 and S3). This meant
that oK simulations were meant to act as tests for the model
as a whole by seeing how the model was able to replicate
the response of the canopy or fluxes to K deficiency. Either
RMSE (single variable to fit) or multiple normalised RMSE
(multiple variables to fit; Eq. S1) were used as goodness-of-
fit indicators when calibrating the model.
The beginning of the simulation was considered to be the
planting date. Tree height at planting was set at 10cm. The
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3105
Figure 2. Outputs of the leaf cohort expansion model over the course of the lifespan of a single leaf from a cohort (produced on day 504 of
the rotation at the Itatinga site) in two contrasted K availabilities, +K(a, b) and oK (c, d); leaf water content, leaf K, and leaf surface at the
individual leaf scale (a, c); total flux of K at the leaf scale showing the transition from K sink (positive flux to the leaf) to K source (negative
flux from the leaf) (b, d). Small negative K fluxes (corresponding to a loss of K from the leaf) during the leaf’s existence are K foliar leaching
fluxes during precipitation events. The grey line represents the fall of the leaf cohort. The quantity of K that is in the leaf at the moment of
leaf fall is added to the K litter pool.
canopy was initialised with a very small, but not null, amount
of leaves: 10 leaves of 30mm2each per metre squared
(equivalent to 0.0003 m2leaf per metre squared of soil). The
soil was divided into 50 layers of either 33cm (for the three
top layers of soil) or 50 cm (the 47 bottom layers) depth
each, and soil properties for each layer were obtained from
Christina et al. (2017). Initial values of water content of the
soil on the planting day were set as measured at the EU-
CFLUX site (Christina et al., 2017). All model runs were
initialised with the amounts of K present in the soil and in
the litter compartment. The amounts of K present in the lit-
ter were determined using measurements of the mass and
elemental dosages of the litter present on the ground at the
beginning of the rotation in the Itatinga experiment, which
amounted to 1.92 gK m−2(Laclau et al., 2010). The amount
of K present in the soil compartment at the start was de-
duced from exchangeable soil K concentrations and bulk soil
density measurements from soil surface to a depth of 18 m
(Maquère, 2008). It amounted to 0.507 gK m−2(it was con-
verted from gK m−3
soil). The simulations were run on the EU-
CFLUX site.
2.9 Model intercomparison
The results of CASTANEA-MAESPA-K were compared to
the MAESPA model (Christina et al., 2015). The simulations
of MAESPA were conducted at the Itatinga site, on the same
rotation as was simulated in this study. MAESPA does not
dynamically simulate canopy dynamics or the effect of K on
diverse processes. Instead the canopy structure and function-
ing of +K and oK stands were the result of a prescribed pa-
rameterisation using yearly values measured at the Itatinga
experimental site (e.g. leaf area, photosynthetic parameters,
and tree height). This model suffered the following short-
comings compared to CASTANEA-MAESPA-K: inability to
simulate a gradient of K availability, inability to simulate dif-
ferent initial conditions, absence of C-allocation sub-model,
absence of K fluxes, and increase in computation time. How-
ever, we considered that it was a good comparison point for
stand fluxes of carbon and water due to both its fine descrip-
tion of canopy structure and functioning and its validation on
soil water content at this site (Christina et al., 2018).
2.10 Sensitivity analysis
A sensitivity analysis was conducted with a one-at-a-time
(OAT) approach, in both K-fertilised (+K) and K-omission
(oK) conditions to test the sensitivity of GPP to the different
processes. The sensitivity of GPP to all the parameters of the
newly introduced sub-models was tested. The method used
was the following: in each fertilisation condition (+K and
oK), the parameter was increased and decreased by 10 %, ex-
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3106 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
Table 1. Mean value of simulated K stocks over the entire rotation.
Stocks (gK m−2)+K oK
Kaccessible
soil 11.18 0.16
Klitter 0.59 0.20
Kcanopy 3.68 0.39
Table 2. Mean value of simulated yearly fluxes of K for two con-
trasted fertilisation regimes: +K and oK.
Fluxes (gK m−2yr−1)+K oK
Kfertiliser→soil 3.60 0
Katmosphere→soil 0.55 0.55
Klitter→soil 1.71 0.66
Kleaves→soil 0.27 0.01
Ksoil→xylem 4.67 1.29
Kleaves→phloem 2.04 0.77
cept the fertilisation parameters which were fixed to their +K
and oK treatment values. The model was then run for each
combination of fertilisation and parameter values. The total
average GPP of the simulated rotation was compared to the
simulated average GPP of the rotation with the same fertili-
sation regime and the initially fixed value of the parameter.
The percentage of difference between +K and oK simula-
tions gave the response of the simulated GPP to the variation
of the chosen parameters.
3 Results
3.1 Ecosystem K cycle during a rotation
The quantity of K accessible in the soil for the plant was on
average 62 times as high in the +K (Fig. 3a) compared to
the oK fertilisation treatments (Fig. 3b). While the K stored
in the canopy was only a small fraction (23 %) of the total
K in the system in the +K stand, leaves accounted for more
than half of the total K stock in the oK stand (52 %). In both
stands, the quantity of K stored in the litter was small, rep-
resenting 3.8 % of total K in +K treatment and 27 % in oK
(Fig. 3,1). In the +K stand, the amount of K in the leaves
increased until 2 years, after which it remained steady up to
harvesting (Fig. 3a). By contrast, the increase only lasted for
1 year in the oK stand and was quickly followed by a strong
decrease (Fig. 3b). The strong decrease in Kleaves was con-
current to an important decrease in Kaccessible
soil , as the initial
litter stock was depleted while the plant demand was still
high and a lower leaf biomass in oK. In the +K stand, the
fertiliser quickly compensates for the decrease in initial litter
K, increasing the Kaccessible
soil to high values.
In the +K treatment, over the course of the rotation, the
fluxes of fertiliser, atmospheric deposition, litter leaching
(Eq. 8), and canopy leaching were respectively 59%, 9 %,
28 %, and 4 % of the total amount of K that entered the soil
(Table 2). In the oK stand, they were respectively 0%, 43 %,
56 %, and 1 % (Table 2). So while the litter stock was small
(Table 1), the cumulated flux of K from the litter to the soil
was important for K cycling in both fertilisation regimes. In
both stands, the resorption flux from leaves (Kleaf→phloem)
was higher than the sum of canopy leaching (Kleaves→soil)
and litter leaching flux (Klitter→soil, Table 2), highlighting the
role of the tree internal K cycling.
In the +K treatment, leaf resorption (Kleaves→phloem) was
equal to 43 % of the average uptake flux (Ksoil→xylem; Ta-
ble 2). In the oK, this proportion was higher (60 %) thus
showing the importance of the internal K recycling for the
maintenance of a suitable K supply for growing organs.
3.2 Leaf cohort model and canopy dynamics
The leaf expansion model was successful in simulating the
influence of K on both the dynamics and maximum value
of the individual leaf area (Fig. 2a, c; Battie-Laclau et al.,
2013). Positive fluxes of K into the leaf took place during the
expansion process (Fig. 2b, c). Foliar leaching, K expulsion
after leaf expansion (Eq. 6), and resorption were responsi-
ble for fluxes of K going out of the leaf across its lifespan
(Fig. 2b, d). This model allowed us to represent leaf K con-
tent in the leaves at the organ scale and also revealed the vari-
ation of K availability at the leaf level during the rotation. In
+K condition, K availability was high during the whole rota-
tion with the symptom area proportion of the canopy always
below 2.5 % (Fig. 5b) throughout the leaf lifespan, reaching
its maximum (LLS, fixed value). On the other hand, in oK
simulations, leaf lifespan was greatly reduced (less than half
of the leaf lifespan of fertilised stands; Fig. 4c), and symptom
proportions reached more than 40 % during a major part of
the rotation (Fig. 4d, 5b). The patterns of the leaf K content
in the different cohorts during the oK rotation had two phases
(Fig. 4c): a first phase of the rotation where soil K bioavail-
ability was high and a second phase with very low K concen-
trations in leaves. This mirrors the K availability in the soil
and litter sub-system (Fig. 3b). The first phase corresponds
to a high initial litter decomposition flux (litter originating
from the preceding rotation which was fertilised with K), in
the second phase the only fluxes of K to the soil were the lit-
ter leaching flux (recycling) and atmospheric deposition (ex-
ternal input). These cumulated fluxes were not sufficient to
satisfy the plant K demand.
The difference of leaf area between the +K and oK sim-
ulated stands was higher than observed in the +K and oK
treatments of the Itatinga fertilisation experiments. The mean
leaf area of the oK stands were 58 % of the leaf area of
the +K stand in the experiment versus 43% in the model
(Fig. 5a). This could be explained by different response to
K deficiency between the genetic material (different euca-
lypt clones) used at EUCFLUX and at Itatinga. Another pos-
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3107
Figure 3. Simulated stocks of K in the soil, litter, fertiliser, and canopy compartments in a non-K-limited (+K) stand (a) and in the same
K-limited (oK) stand (b). Note differences of the yaxis scales for better visualisation.
sibility was an underestimation of K availability in the oK
stand in our simulations. For example, a small change in
the mineral weathering flux from 0 to a realistic value of
0.3 gK m−2yr−1(Cornut et al., 2021) led to the simulated
leaf area in the oK stand being 53 % of the +K stand (not
shown).
In the oK condition, symptoms appeared very early during
the leaves’ lifespan (Fig. 4d). The proportion of symptomatic
leaf area was slightly higher in the simulations of the EU-
CFLUX site than measurements at the Itatinga site (Fig. S7).
This could be due to an overestimation of the leaves’ limita-
tion by K or a difference in response of the genetic material
to K availability.
3.3 Carbon and water fluxes
Simulated GPP was greatly reduced under oK conditions
(Fig. 6a), and the cumulated GPP in the oK stand was only
50 % of the +K stand on average (Table 3). Seasonal fluc-
tuations of GPP between dry and wet seasons were clearly
visible in both simulations; however the seasonal variability
was higher in the +K stand (Fig. 6a) due to lower access to
soil water in the +K stand as a result of higher ETR resulting
in faster deep-soil water depletion (Fig. 6b). The difference
of GPP between fertilisation regimes was not constant dur-
ing the rotation. During the first phase (i.e. the first year),
the difference was small due to similar low leaf areas in both
fertilisation conditions resulting in low K demand, fulfilled
by sufficient K availability for both treatments (Fig. 4a, c).
The difference was also quite small during the major 2014
drought (Fig. 6a) where water limitation dominated in the
+K stand. The simulated GPPs were similar to both mea-
surements (Epron et al., 2012) and simulations conducted at
Itatinga with the MAESPA model (Christina et al., 2015) (Ta-
ble 3).
Our simulations showed reduced evapotranspiration un-
der K deficiency (Fig. 6b), which was expected, since K
deficiency had a strong impact on leaf area (Fig. 5a). We
compared our transpiration simulation results with those ob-
tained using the MAESPA model at the Itatinga oK stand.
The MAESPA-simulated transpiration values had been vali-
dated using sap-flow measurements. While in the first part of
the rotation the difference between treatments simulated by
our model was lower than those simulated by MAESPA, in
the following years our simulations were close to MAESPA
results (Table 4). Total 5-year cumulated transpiration in the
oK plot was 54 % of that of the +K plot in our simulation
of the EUCFLUX site. This was a slightly higher proportion
than for GPP; i.e. GPP was more impacted than transpiration
by K deficit. As a consequence, the simulated WUE for GPP
was higher in +K condition in our simulations (Table 4).
3.4 Sensitivity analysis
Sensitivity analysis was done separately for a K fertilised and
the K omission stand. The simulated GPP cumulated over the
whole simulation period of 5 years was highly sensitive to
few sub-model parameters, but this sensitivity was strongly
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3108 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
Figure 4. Outputs of the leaf cohort model in two contrasted K fertilisation regimes. The K content present in each individual leaf of the
cohort is represented through the lifespan of a cohort (xaxis) for the different cohort created along the first 60 months of the rotation (a, c).
The symptom area proportion for each leaf of the cohort is also represented (b, d). Top subplots (a, b) were simulated in +K conditions,
while bottom subplots were oK simulations (c, d).
Table 3. Annual GPP at the study sites, under contrasted K supply regimes. Values from Epron et al. (2012) were inferred from fluxes and
biomass increment measurements obtained from a previous fertilisation experiment at the Itatinga site. Values from Christina et al. (2015)
were simulated by the MAESPA model. Percentages in parentheses indicate the ratio of GPP between the oK and +K treatments for each
experiment. The data presented are different from those on Fig. 6b that display evapotranspiration.
Estimated GPP (Itatinga) Modelled GPP (Itatinga) Modelled GPP (EUCFLUX)
from Epron et al. (2012) from Christina et al. (2015) in this study
(gC m−2yr−1) (gC m−2yr−1) (gC m−2yr−1)
Age (years) +K–oK +K–oK +K–oK
0→1 . . . –. . . 1300–800 (61 %) 1129–1083 (95 %)
1→2 . . . –. . . 3500–2500 (71 %) 3926–2519 (64 %)
2→3 . . . –. . . 4600–2900 (63 %) 4541–1782 (39 %)
3→4 . . . –. . . . . . –. . . 3971–1636 (41 %)
4→5 4440–2540 (57 %) . . . –. . . 3653–1670 (45 %)
dependent on the fertilisation treatment (Fig. 7a). Among the
tested parameters, in the +K condition, GPP was sensitive to
parameters related to the leaf phenology, especially the ones
driving maximum leaf area and maximum leaf lifespan. In-
crease in maximum leaf area (LAmax), number of leaves pro-
duced by height increment (κ) and maximum lifespan (LLS)
parameters resulted in GPP increases in the +K simulations.
These parameters had an impact on the leaf area of trees thus
directly affecting photosynthetic area. This shows that un-
der non-limiting K availability (+K conditions), the simu-
lated GPP was mainly limited by leaves developmental as-
pects among the parameters tested here, i.e. the ones directly
involved in processes related to K cycling.
Under severe K deficiency (oK), simulated GPP was sen-
sitive to a greater number of parameters, but a pattern was
still visible. In this case, variations in the parameters control-
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3109
Figure 5. Simulated leaf area index in both the fertilised +K and non-fertilised oK treatments, and the leaf area index measured at the Itatinga
experiment and at the eddy covariance site EUCFLUX (a). Canopy average proportion of leaf area with symptoms in both fertilisation
treatments (b).
Table 4. Annual transpiration fluxes for contrasting K supply regimes both in our study and in a previous modelling work that used the
MAESPA model (Christina et al., 2018). Percentages between parentheses indicate the ratio of transpiration between the oK and +K treat-
ments for each experiment.
Modelled Transpiration (Itatinga) Modelled transpiration WUEGPP this study
in Christina et al. (2018) (EUCFLUX) in this study (mmolC molH2O−1)
(mm yr−1) (mm yr−1)
Age (years) +K–oK +K–oK +K–oK
0.5 →1.5 947–654 (69 %) 969–858 (88 %) 4.69–4.13
1.5 →2.5 1365–881 (64 %) 1605–791 (49 %) 4.10–3.73
2.5 →3.5 1438–753 (52 %) 1344–649 (48 %) 4.38–3.95
3.5 →4.5 1323–774 (58 %) 1458–678 (46 %) 4.05–3.69
ling the values of K inputs to the ecosystem (Katmosphere→soil,
Kini
litter,Kini
soil) produced a strong response in simulated GPP,
highlighting the strong limitation of GPP by K availability.
The amplitude of the response was in line with their respec-
tive contribution to the total amount of K entering into the
system throughout the rotation (Table 2). In the oK condition,
contrary to +K, the model was not sensitive to the parameter
controlling maximum leaf lifespan (LLS; Fig. 7). Indeed, the
maximum leaf lifespan was almost never reached because of
earlier leaf fall due to K limitation (Fig. 4c). Other parame-
ters (t50LA,kLA) controlling maximum leaf growth also had
a much lower impact for similar reasons. Sensitivity of sim-
ulated GPP to the leaf maximum individual area (LAmax) in
the oK stand was high, as in the +K case. Indeed, this pa-
rameter was used both in the +K and oK case because the
area increment, depending on this target value, was modu-
lated when a leaf cohort experienced a K deficit (Eqs. 2 and
30). This led to a variation in leaf area of each cohort, which
directly affected the GPP. The second most important leaf
parameter in the oK stand was the resistance to K flux from
the leaf to the phloem (Rleaf→phloem; Fig. 7b). This parameter
was important, since it controlled the competition for the K
resource between new leaves (demanding K) and old leaves
(providing K through resorption). In our simulations, an in-
crease (+10 % in Fig. 7b) in resistance to K flux between the
leaves and the phloem had a positive impact on GPP, at least
in the range of values considered. Indeed, increasing the re-
sistance (Rleaf→phloem) led to a higher conservation of K in
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3110 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
Figure 6. Simulated and measured daily gross primary productivity
(a) and evapotranspiration (b) fluxes simulated in two stands with
contrasted fertilisation regimes. The measurements were performed
continuously using the eddy covariance method at the EUCFLUX
site (a +K stand, fully fertilised). A rolling average of 30d was
applied to the observed and simulated time series for the sake of
clarity.
the leaves, which kept the leaf K concentration longer above
the leaf shedding K threshold, which increased the leaf re-
alised lifespan, which in turn increased canopy area. Since
LAI in the oK stand was low (Fig. 6a), a small increase in
LAI can have an important impact on stand GPP. [K]min
is the K concentration value below which leaves start their
senescence. An increase of this value caused earlier leaf fall
because this value was reached sooner, and GPP therefore
decreased. Finally, the parameter related to symptoms area
SPmax was also sensible in the model; i.e. the GPP is reduced
when the symptoms of area increase.
4 Discussion
In this work, we developed a process-based model simulating
the influence of K on the gross primary productivity and tran-
spiration fluxes of tropical eucalypt plantations. Such models
have rarely been published in the literature, and we identified
it “a worthwhile endeavour” (Reed et al., 2015) owing to the
importance of K limitation of productivity in forests around
the world (Sardans and Peñuelas, 2015). We used tropical
eucalypt plantations as our primary study system; since nu-
trient limitation has been extensively studied there, they are
typically highly fertilised, and K-omission experiments show
a very strong response of wood productivity to K deficiency
(Laclau et al., 2010).
Our K model incorporates parts of the K cycle that were
essential in determining K availability at the plant level. We
focused on the modelling of the carbon-source activity on
canopy processes and fluxes, starting with the demography
of leaves and the impact of K availability on their function-
ing. In particular, we first considered the impacts of K on
leaf development, photosynthetic capacity, and senescence.
We included processes that we identified as central (Cornut
et al., 2021) regarding the K limitation of GPP in these plan-
tations. While adding processes to a mechanistic model is
pertinent from a realism perspective, one must consider if the
implementation of new processes increases or decreases the
predictive power of the model in a given context (Famiglietti
et al., 2021). Here, the model additions were clearly neces-
sary, since the CASTANEA model, into which we developed
the K modules, was initially incapable of reproducing the ef-
fect of K limitation on GPP, and no mechanistic model of
the effect of K on plant productivity at the stand level ex-
isted. This development also broadly followed several of the
guidelines posited by Famiglietti et al. (2021) in their pa-
per addressing the question of models’ structural complexity.
These points are as follows: (1) we used datasets (here mul-
tiple experiments over multiple rotations) to constrain model
parameters, (2) the new developments led to increased fore-
cast ability (since no forecast of K deficiency was previously
possible), and (3) we sought to calibrate unmeasured param-
eters. We adopted a reductionist approach, typical of the de-
velopment of mechanistic model, by formulating and param-
eterising the model on dedicated experiments conducted at
the organ scale. Only a few parameters were calibrated on
carbon and water fluxes measured at the ecosystem scale.
It is noticeable that the model was calibrated in a fully fer-
tilised stand and then allowed to run in a virtual K omission
stand with, as the only difference, a reduced amount of K fer-
tiliser brought the first months after planting. The simulations
showed a strong impact on C and water fluxes.
For K supplied trees, our model was able to simulate GPP
and water fluxes close to the measured flux values at the EU-
CFLUX experimental site, both in terms of seasonality and
magnitude (Fig. 6), with a calibration of the canopy genera-
tion model in fully fertilised conditions and the use of mea-
sured parameters (Table S3). Compared to our model, the
MAESPA model uses a much finer spatial scale to model
water and carbon fluxes (Christina et al., 2018, 2015) in both
fertilisation regimes, but the parameterisation of the model is
different in +K and oK; i.e. it does not simulate the K cy-
cling and its impact on the parameters (which is a feature of
CASTANEA-MAESPA-K). The MAESPA model has no leaf
generation module, and the canopy structure is prescribed
from measurements. It is possible that the CASTANEA-
MAESPA-K model presented here lost some accuracy in the
prediction of carbon and water fluxes compared to MAESPA
alone, due to the inclusion of new processes linked both to
canopy generation and to K cycle instead of a direct param-
eter forcing with measurements. It also did not use the 3D
representation of trees of MAESPA, which had probably im-
proved the simulation of fluxes during the first year of the ro-
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3111
Figure 7. Sensitivity of GPP cumulated over a rotation to a ±10% change in parameters related to soil availability, diffusion resistances, and
response of leaves development to K. For each parameter, the sensitivity analysis was performed for the two contrasting K supply regimes
(+K and oK). Note differences on the yaxes scales for the sake of clarity.
tation, before canopy closure (Christina et al., 2018). At the
rotation scale however, the differences between the measured
accumulated GPP and the simulated accumulated GPP flux
are small (Fig. S2). While at a different scale, the new de-
velopments in the ORCHIDEE-MICT-BIOENERGY model
(Li et al., 2018) resolved the issue of an overestimation bias
on productivity of eucalypt plantations, the intersite variabil-
ity was not well represented (see Fig. 11 in Li et al., 2018).
Moreover, the ORCHIDEE-MICT-BIOENERGY presented
no bias for fully fertilised sites, but there was an overestima-
tion bias for sites with no known fertilisation regime. This
strongly suggests that the model failed to account for nutri-
ent limitation of productivity. CASTANEA-MAESPA-K is a
first step in simulating the limitation of forest productivity
by base cations. The importance of N (Du et al., 2020) and P
(Hou et al., 2020) limitation of forest productivity has been
recognised by their inclusion in terrestrial biosphere models
(TBMs) (Goll et al., 2017). This has allowed for the estima-
tion of the N and P limitation of net primary productivity at
the global scale (Ellsworth et al., 2022). The importance of
base cation limitation is increasingly recognised for tropical
forests (Bauters et al., 2022), and the progressive inclusion of
K, Mg, and Ca in TBMs could provide clues on the response
of forest productivity to increasing CO2levels.
The difference in cumulated GPP between the +K and oK
stands simulated by the model was large on average but var-
ied during the rotation. In the first year, the difference in GPP
between oK and +K (Table 3) was underestimated in our
model compared to Christina et al. (2015). The leaf cohort
model also showed that leaves were not K-limited at the be-
ginning of the oK stand rotation (Fig. 4c). Both leaf K con-
tent and symptomatic leaf area showed similar dynamics be-
tween the simulated oK and +K stands until around 1 year
of age (Fig. 6b). These results suggest that until this time,
K was not more limiting in oK than in +K. The simulated
plant available K in the soil was similar in both treatments at
the beginning of the rotations, which suggests that either K
availability was in fact high at the beginning of the oK sim-
ulation (through litter remaining at harvest and K available
in the soil from the previous rotation) and/or that our model
overestimated K soil access in the first year.
The simulated water-use efficiencies (WUEs; Table 4)
were in the range of the spectrum for C3woody plants (Lam-
bers and Oliveira, 2019) and resulted from simulated tran-
spiration and GPP fluxes that compared well with observa-
tions (Tables 4 and 3). Our simulations showed a decrease
of both GPP and transpiration in the oK stand that was con-
sistent with evidence from the MAESPA model (Christina
et al., 2015, 2018) and from experiments (Epron et al., 2012).
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3112 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
WUEGPP was higher in the simulated +K treatment than in
the oK treatment (Table 4). While not directly comparable,
experimental data showed a similar pattern for wood WUE
but differed on leaf intrinsic WUE, for which no effect was
reported (Battie-Laclau et al., 2016). The observed difference
was small, and in their study, Battie-Laclau et al. (2016) ex-
plained the difference between wood WUE and intrinsic leaf
WUE by differences in the post-GPP processes of carbon al-
location in +K vs. oK. This could suggest that our approach
of restricting the effects of symptoms to the photosynthetic
capacity was insufficient and that a direct effect on stomatal
response or mesophyll conductance is necessary. Part of the
effects of K on leaf functioning could also be ignored by
our approach of direct proportionality between the area of
symptoms and the reduction of leaf photosynthetic capacity.
Studying the response of leaf functioning to a gradient of in-
dividual leaf K content (Basile et al., 2003; Shen et al., 2018)
may be useful to diminish the uncertainty regarding this re-
sponse (see Sect. 6.6) and increase model genericity.
The sub-model we implemented for the simulation of plant
K uptake was a simple demand model, dampened by a re-
sistance meant to represent diffusion and sorption/desorp-
tion processes that impede the uptake of K ions by the
plant from the soil. It was similar to models used success-
fully in ForNBM (Zhu et al., 2003) and ForSVA (Arp and
Oja, 1997) that are based on the law of diminishing returns
(van den Driessche, 1974). Except for the soil access equa-
tion (Eq. 10), our model did not consider K-uptake kinetics
to depend on root density. This was in part due to the highly
dynamic growth of eucalypt trees that go from saplings to
25–30 m trees in less than 6 years (the same being true for
roots down to 16m depth; Christina et al., 2011). However,
the sensitivity analysis showed that GPP was not greatly af-
fected by the resistance to uptake in both fertilisation con-
ditions. This is in accordance with results from the Itatinga
site, where K+ions appeared weakly sorbed to this sandy
soil; hence the process of diffusion was probably not limiting
(Cornut et al., 2021). Moreover, uptake of K by roots can take
place directly in the litter (Laclau et al., 2004) thus bypass-
ing the soil entirely. Taking K–soil interactions into account
might however be necessary if one were studying leaching of
K ions in the soil.
The absence of a sub-model for deep leaching of K
in the soil, while a suitable assumption when applying
CASTANEA-MAESPA-K to our two sites with very deep
Ferralsols (Maquère, 2008; Caldeira Filho et al., 2023),
might not hold in other ecosystems with shallower soils or
less cationic exchange capacity. This process was not in the
scope of this study due to the added complexity of repre-
senting K–soil exchange dynamics and the absence of suf-
ficient measurement to successfully parameterise the sub-
model. The importance of the accurate measurement of K
sources in the system was underlined by the results of the
sensitivity analysis. The simulated GPP of the oK stand was
sensitive to variables relating to K inputs. The GPP showed a
strong response to small changes in the yearly influx from at-
mospheric deposition. This mirrors, e.g. observations of the
response of forest photosynthetic capacity to N deposition
(Fleischer et al., 2013) and simulations of the response of
GPP in Afrotropical forests to increases in P deposition (Goll
et al., 2023). The response of GPP to initial K litter stock also
underlined the importance of harvest residues in the mainte-
nance of plot fertility.
It was apparent that the model shifted from developmental
(leaf production, maximum leaf lifespan, leaf area) and pedo-
climatic limitations of GPP in the +K treatment to biogeo-
chemical limitations in oK. For example, the level of min-
eral weathering had an important impact on the GPP flux
of the oK stand (not shown here; Cornut et al., 2022), but
uncertainty regarding this flux is high (Cornut et al., 2021;
de Oliveira et al., 2021; Pradier et al., 2017). We believe
these results confirm the importance of studying biological
weathering of minerals in situations of strong K limitation in
forests.
The analysis of the model also showed the importance
of internal K cycling, especially the resorption flux be-
tween the leaves and the phloem. The intense cycling of
K in plants has been amply demonstrated (Marschner and
Cakmak, 1989). Measurements are still lacking to evaluate
whether our phloem demand simplification to explain the
variation in leaf K content is true in different conditions.
5 Conclusions and perspectives
This study is the first attempt to simulate the K cycle in a for-
est ecosystem and its link to the carbon and water balances
at different time and space scales. It was developed based on
data and processes observed in eucalypt fast-growing planta-
tions under contrasting fertilisation regimes. The model was
tested against stand-scale measurements and showed reli-
able results for both K-fertilised and K-omission simulations.
First analyses show that K amounts present at the beginning
of the rotation (in litter, soil, or fertilisation) and atmospheric
deposition are essential to explain the overall amounts of K
in foliage. Then the internal K cycling dominates the K avail-
ability to leaves, which in turn influence strongly leaf devel-
opment, leaf area index, and GPP.
The coupled carbon–water–potassium forest process-
based model developed in this study represents an important
step in the endeavour to understand the nutrient limitation of
forest productivity. This study, focusing on the canopy and
C-source processes, is followed by a second part (in a com-
panion paper) which will investigate the C-sink limitation of
growth under low K availability. It also provides a frame-
work for the development of modules that will incorporate
other ionic nutrients such as Mg or Ca. The leaf cohort model
developed is also a good starting point for accurately simu-
lating nutrient fluxes in tropical forests that follow a contin-
uous phenology. These modelling frameworks can then be
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3113
adapted to other similar systems. This work was enabled by
long-term omission experiments and detailed data collection
at these sites (Cornut et al., 2021). This further underlines the
necessity of these stand-scale manipulation experiments for
nutrient modelling work.
Data availability. Data are not freely available due to private fund-
ing of experimental sites but are available upon request.
Supplement. The supplement related to this article is available on-
line at: https://doi.org/10.5194/bg-20-3093-2023-supplement.
Author contributions. IC carried out the development of the model
and wrote the original draft of the paper. GlM and ND supervised
the work, participated in the conceptualisation of the model, and re-
viewed the original draft of the paper. JPL, YN, and JG participated
in the acquisition of the data and reviewed the original draft of the
paper. VFD carried out the photosynthesis experiments. All authors
provided critical feedback and helped shape the research, analysis,
and paper.
Competing interests. The contact author has declared that none of
the authors has any competing interests.
Disclaimer. Publisher’s note: Copernicus Publications remains
neutral with regard to jurisdictional claims in published maps and
institutional affiliations.
Special issue statement. This article is part of the special issue
“Ecosystem experiments as a window to future carbon, water, and
nutrient cycling in terrestrial ecosystems”. It is not associated with
a conference.
Acknowledgements. Ivan Cornut was funded by the ANR under
the “Investissements d’avenir” programme and by the Centre de
coopération Internationale en Recherche Agronomique pour le
Développement (CIRAD). The data acquired on Eucalyptus stands
at Itatinga station, Brazil, and partly re-analysed here, were funded
by Universidade de São Paulo, CIRAD, Agence Nationale de la
Recherche, the Agropolis Foundation, and from the support of
the Brazilian state (Programa de Cooperacão internacional capes/-
Fundacão AGROPOLIS 017/2013). We are grateful to the staff at
the Itatinga Experimental Station, in particular, Rildo Moreira e
Moreira (ESALQ, USP) and Eder Araujo da Silva, for their tech-
nical support. The EUCFLUX 1 project was a cooperative pro-
gramme with the participation of Arcelor Mittal, Cenibra, Bahia
Specialty Cellulose, Duratex, Fibria, International Paper, Klabin,
Suzano, and Vallourec Florestal, coordinated by the Forestry Sci-
ence and Research Institute – IPEF (https://www.ipef.br/, last ac-
cess: 16 March 2023). The data acquired on the response of photo-
synthesis to leaf K were funded and conducted by Suzano. We thank
Daniel Goll and one anonymous reviewer for their very meticulous
evaluation of the paper and relevant remarks that helped greatly in
improving the article.
Financial support. This research has been supported by the Agence
Nationale de la Recherche (grant nos. ANR-16-CONV-0003, ANR-
13-AGRO-0005, and ANR-10-LabX-0001-01).
Review statement. This paper was edited by Silvia Caldararu and
reviewed by Daniel Goll and one anonymous referee.
References
Arp, P. A. and Oja, T.: A forest soil vegetation atmosphere
model (ForSVA), I: Concepts, Ecol. Model., 95, 211–224,
https://doi.org/10.1016/S0304-3800(96)00036-1, 1997.
Attia, A., Nouvellon, Y., Cuadra, S., Cabral, O., Laclau, J.-P.,
Guillemot, J., Campoe, O., Stape, J.-L., Galdos, M., Lampar-
elli, R., and le Maire, G.: Modelling carbon and water bal-
ance of Eucalyptus plantations at regional scale: Effect of cli-
mate, soil and genotypes, Forest Ecol. Manag., 449, 117460,
https://doi.org/10.1016/j.foreco.2019.117460, 2019.
Baldocchi, D. D.: Assessing the eddy covariance technique
for evaluating carbon dioxide exchange rates of ecosystems:
past, present and future, Glob. Change Biol., 9, 479–492,
https://doi.org/10.1046/j.1365-2486.2003.00629.x, 2003.
Basile, B., Reidel, E. J., Weinbaum, S. A., and DeJong, T. M.: Leaf
potassium concentration, CO2exchange and light interception
in almond trees (Prunus dulcis (Mill) D.A. Webb), Sci. Hortic.-
Amsterdam, 98, 185–194, https://doi.org/10.1016/S0304-
4238(02)00214-5, 2003.
Battie-Laclau, P., Laclau, J.-P., Piccolo, M. d. C., Arenque, B. C.,
Beri, C., Mietton, L., Muniz, M. R. A., Jordan-Meille, L., Buck-
eridge, M. S., Nouvellon, Y., Ranger, J., and Bouillet, J.-P.: In-
fluence of potassium and sodium nutrition on leaf area com-
ponents in Eucalyptus grandis trees, Plant Soil, 371, 19–35,
https://doi.org/10.1007/s11104-013-1663-7, 2013.
Battie-Laclau, P., Delgado-Rojas, J. S., Christina, M., Nouvellon,
Y., Bouillet, J.-P., Piccolo, M. d. C., Moreira, M. Z., Gonçalves,
J. L. d. M., Roupsard, O., and Laclau, J.-P.: Potassium fer-
tilization increases water-use efficiency for stem biomass pro-
duction without affecting intrinsic water-use efficiency in Eu-
calyptus grandis plantations, Forest Ecol. Manag., 364, 77–89,
https://doi.org/10.1016/j.foreco.2016.01.004, 2016.
Battie-Laclau, P., Laclau, J.-P., Beri, C., Mietton, L., Muniz, M.
R. A., Arenque, B. C., Piccolo, M. D. C., Jordan-Meille, L.,
Bouillet, J.-P., and Nouvellon, Y.: Photosynthetic and anatom-
ical responses of Eucalyptus grandis leaves to potassium and
sodium supply in a field experiment, Plant Cell Environ., 37, 70–
81, https://doi.org/10.1111/pce.12131, 2014a.
Battie-Laclau, P., Laclau, J.-P., Domec, J.-C., Christina, M., Bouil-
let, J.-P., Piccolo, M. d. C., Gonçalves, J. L. d. M., Moreira, R.
M. E., Krusche, A. V., Bouvet, J.-M., and Nouvellon, Y.: Effects
of potassium and sodium supply on drought-adaptive mecha-
nisms in Eucalyptus grandis plantations, New Phytol., 203, 401–
413, https://doi.org/10.1111/nph.12810, 2014b.
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3114 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
Bauters, M., Janssens, I. A., Wasner, D., Doetterl, S., Vermeir,
P., Griepentrog, M., Drake, T. W., Six, J., Barthel, M., Baum-
gartner, S., Van Oost, K., Makelele, I. A., Ewango, C., Ver-
heyen, K., and Boeckx, P.: Increasing calcium scarcity along
Afrotropical forest succession, Nat. Ecol. Evolut., 6, 1122–1131,
https://doi.org/10.1038/s41559-022-01810-2, 2022.
Bonneau, M.: Quelques résultats d’essai de fertilisation sur Épicéa
dans le Massif central, Revue Forestière Française, 24, 354–363,
https://doi.org/10.4267/2042/20633, 1972.
Caldeira Filho, A., Krushe, A. V., Mareschal, L., da Silva, P., Nou-
vellon, Y., Campoe, O., Stape, J. L., Montebelo, A., Formaglio,
G., le Maire, G., Guillemot, J., Ranger, J., and Laclau, J.-P.: Very
Low Nutrient Losses by Deep Leaching after Clearcutting Com-
mercial Eucalyptus Plantations in Brazil, Forest Ecol. Manag.,
534, 120866, https://doi.org/10.2139/ssrn.4270148, 2023.
Christina, M., Laclau, J.-P., Gonçalves, J. L. M., Jourdan,
C., Nouvellon, Y., and Bouillet, J.-P.: Almost symmetri-
cal vertical growth rates above and below ground in one
of the world’s most productive forests, Ecosphere, 2, 1–10,
https://doi.org/10.1890/ES10-00158.1, 2011.
Christina, M., Maire, G. L., Battie-Laclau, P., Nouvellon, Y., Bouil-
let, J.-P., Jourdan, C., Gonçalves, J. L. d. M., and Laclau, J.-
P.: Measured and modeled interactive effects of potassium defi-
ciency and water deficit on gross primary productivity and light-
use efficiency in Eucalyptus grandis plantations, Glob. Change
Biol., 21, 2022–2039, https://doi.org/10.1111/gcb.12817, 2015.
Christina, M., Nouvellon, Y., Laclau, J.-P., Stape, J. L., Bouillet,
J.-P., Lambais, G. R., and Maire, G. L.: Importance of deep wa-
ter uptake in tropical eucalypt forest, Funct. Ecol., 31, 509–519,
https://doi.org/10.1111/1365-2435.12727, 2017.
Christina, M., le Maire, G., Nouvellon, Y., Vezy, R., Bordon, B.,
Battie-Laclau, P., Gonçalves, J. L. M., Delgado-Rojas, J. S.,
Bouillet, J. P., and Laclau, J. P.: Simulating the effects of dif-
ferent potassium and water supply regimes on soil water con-
tent and water table depth over a rotation of a tropical Eu-
calyptus grandis plantation, Forest Ecol. Manag., 418, 4–14,
https://doi.org/10.1016/j.foreco.2017.12.048, 2018.
Cornut, I., Le Maire, G., Laclau, J.-P., Guillemot, J., Mareschal,
L., Nouvellon, Y., and Delpierre, N.: Potassium limita-
tion of wood productivity: A review of elementary pro-
cesses and ways forward to modelling illustrated by Eu-
calyptus plantations, Forest Ecol. Manag., 494, 119275,
https://doi.org/10.1016/j.foreco.2021.119275, 2021.
Cornut, I., le Maire, G., Laclau, J.-P., Guillemot, J., Nouvel-
lon, Y., and Delpierre, N.: Potassium limitation of forest
productivity – Part 2: CASTANEA-MAESPA-K shows a re-
duction in photosynthesis rather than a stoichiometric lim-
itation of tissue formation, Biogeosciences, 20, 3119–3135,
https://doi.org/10.5194/bg-20-3119-2023, 2023.
Crockford, R. H., Richardson, D. P., and Sageman, R.: Chem-
istry of rainfall, throughfall and stemflow in a eucalypt forest
and a pine plantation in south-eastern Australia: 2. Throughfall,
Hydrol. Process., 10, 13–24, https://doi.org/10.1002/(SICI)1099-
1085(199601)10:1<13::AID-HYP296>3.0.CO;2-5, 1996.
Cunha, H. F. V., Andersen, K. M., Lugli, L. F., Santana, F. D.,
Aleixo, I. F., Moraes, A. M., Garcia, S., Di Ponzio, R., Men-
doza, E. O., Brum, B., Rosa, J. S., Cordeiro, A. L., Portela, B.
T. T., Ribeiro, G., Coelho, S. D., de Souza, S. T., Silva, L. S.,
Antonieto, F., Pires, M., Salomão, A. C., Miron, A. C., de As-
sis, R. L., Domingues, T. F., Aragão, L. E. O. C., Meir, P., Ca-
margo, J. L., Manzi, A. O., Nagy, L., Mercado, L. M., Hartley,
I. P., and Quesada, C. A.: Direct evidence for phosphorus lim-
itation on Amazon forest productivity, Nature, 608, 558–562,
https://doi.org/10.1038/s41586-022-05085-2, 2022.
Davi, H., Dufrêne, E., Francois, C., Le Maire, G., Loustau, D., Bosc,
A., Rambal, S., Granier, A., and Moors, E.: Sensitivity of wa-
ter and carbon fluxes to climate changes from 1960 to 2100 in
European forest ecosystems, Agr. Forest Meteorol., 141, 35–56,
https://doi.org/10.1016/j.agrformet.2006.09.003, 2006.
Delpierre, N., Soudani, K., François, C., Le Maire, G., Bern-
hofer, C., Kutsch, W., Misson, L., Rambal, S., Vesala,
T., and Dufrêne, E.: Quantifying the influence of cli-
mate and biological drivers on the interannual variability
of carbon exchanges in European forests through process-
based modelling, Agr. Forest Meteorol., 154/155, 99–112,
https://doi.org/10.1016/j.agrformet.2011.10.010, 2012.
de Oliveira, F. B., Carneiro, S. H., de Souza, N. F., Horta, B. M.,
da Silva, I. R., Fontes, M. P. F., and Valadares, S. V.: Soil potas-
sium dynamics in the eucalypt rhizosphere, Trees, 35, 1411–
1415, https://doi.org/10.1007/s00468-021-02153-4, 2021.
Du, E., Terrer, C., Pellegrini, A. F. A., Ahlström, A., van Lissa, C. J.,
Zhao, X., Xia, N., Wu, X., and Jackson, R. B.: Global patterns of
terrestrial nitrogen and phosphorus limitation, Nat. Geosci., 13,
221–226, https://doi.org/10.1038/s41561-019-0530-4, 2020.
Dufrêne, E., Davi, H., François, C., Maire, G. l., Dantec,
V. L., and Granier, A.: Modelling carbon and water cy-
cles in a beech forest: Part I: Model description and uncer-
tainty analysis on modelled NEE, Ecol. Model., 185, 407–436,
https://doi.org/10.1016/j.ecolmodel.2005.01.004, 2005.
Duursma, R. A. and Medlyn, B. E.: MAESPA: a model to study
interactions between water limitation, environmental drivers and
vegetation function at tree and stand levels, with an example ap-
plication to [CO2]×drought interactions, Geosci. Model Dev.,
5, 919–940, https://doi.org/10.5194/gmd-5-919-2012, 2012.
Ellsworth, D. S., Crous, K. Y., De Kauwe, M. G., Verryckt, L. T.,
Goll, D., Zaehle, S., Bloomfield, K. J., Ciais, P., Cernusak,
L. A., Domingues, T. F., Dusenge, M. E., Garcia, S., Guerrieri,
R., Ishida, F. Y., Janssens, I. A., Kenzo, T., Ichie, T., Medlyn,
B. E., Meir, P., Norby, R. J., Reich, P. B., Rowland, L., Santi-
ago, L. S., Sun, Y., Uddling, J., Walker, A. P., Weerasinghe, K.
W. L. K., van de Weg, M. J., Zhang, Y.-B., Zhang, J.-L., and
Wright, I. J.: Convergence in phosphorus constraints to photo-
synthesis in forests around the world, Nat. Commun., 13, 5005,
https://doi.org/10.1038/s41467-022-32545-0, 2022.
Epron, D., Laclau, J.-P., Almeida, J. C. R., Gonçalves, J. L. M.,
Ponton, S., Sette, C. R., Delgado-Rojas, J. S., Bouillet, J.-P.,
and Nouvellon, Y.: Do changes in carbon allocation account
for the growth response to potassium and sodium applications
in tropical Eucalyptus plantations?, Tree Physiol., 32, 667–679,
https://doi.org/10.1093/treephys/tpr107, 2012.
Epron, D., Cabral, O. M. R., Laclau, J.-P., Dannoura, M., Packer,
A. P., Plain, C., Battie-Laclau, P., Moreira, M. Z., Trivelin, P.
C. O., Bouillet, J.-P., Gérant, D., and Nouvellon, Y.: In situ
13CO2pulse labelling of field-grown eucalypt trees revealed
the effects of potassium nutrition and throughfall exclusion on
phloem transport of photosynthetic carbon, Tree Physiol., 36, 6–
21, https://doi.org/10.1093/treephys/tpv090, 2016.
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3115
Famiglietti, C. A., Smallman, T. L., Levine, P. A., Flack-Prain, S.,
Quetin, G. R., Meyer, V., Parazoo, N. C., Stettz, S. G., Yang,
Y., Bonal, D., Bloom, A. A., Williams, M., and Konings, A. G.:
Optimal model complexity for terrestrial carbon cycle prediction,
Biogeosciences, 18, 2727–2754, https://doi.org/10.5194/bg-18-
2727-2021, 2021.
Farquhar, G. D., Caemmerer, S. V., and Berry, J. A.:
A biochemical model of photosynthetic CO2assim-
ilation in leaves of C3species, Planta, 149, 78–90,
https://doi.org/10.1007/BF00386231, 1980.
Fleischer, K., Rebel, K. T., van der Molen, M. K., Erisman,
J. W., Wassen, M. J., van Loon, E. E., Montagnani, L., Gough,
C. M., Herbst, M., Janssens, I. A., Gianelle, D., and Dolman,
A. J.: The contribution of nitrogen deposition to the photosyn-
thetic capacity of forests, Global Biogeochem. Cy., 27, 187–199,
https://doi.org/10.1002/gbc.20026, 2013.
Goll, D. S., Brovkin, V., Parida, B. R., Reick, C. H., Kattge, J., Re-
ich, P. B., van Bodegom, P. M., and Niinemets, U.: Nutrient lim-
itation reduces land carbon uptake in simulations with a model
of combined carbon, nitrogen and phosphorus cycling, Bio-
geosciences, 9, 3547–3569, https://doi.org/10.5194/bg-9-3547-
2012, 2012.
Goll, D. S., Vuichard, N., Maignan, F., Jornet-Puig, A., Sar-
dans, J., Violette, A., Peng, S., Sun, Y., Kvakic, M., Guim-
berteau, M., Guenet, B., Zaehle, S., Penuelas, J., Janssens, I.,
and Ciais, P.: A representation of the phosphorus cycle for OR-
CHIDEE (revision 4520), Geosci. Model Dev., 10, 3745–3770,
https://doi.org/10.5194/gmd-10-3745-2017, 2017.
Goll, D. S., Bauters, M., Zhang, H., Ciais, P., Balkanski, Y.,
Wang, R., and Verbeeck, H.: Atmospheric phosphorus de-
position amplifies carbon sinks in simulations of a tropi-
cal forest in Central Africa, New Phytol., 237, 2054–2068,
https://doi.org/10.1111/nph.18535, 2023.
Gonçalves, J. L. d. M.: Nutrição e fertilização florestal, IPEF, ISBN:
9788590135814, 2000.
Greenwood, D. J. and Karpinets, T. V.: Dynamic model for
the effects of K-fertilizer on crop growth, K-uptake and
soil-K in arable cropping. 1. Description of the model,
Soil Use Manag., 13, 178–183, https://doi.org/10.1111/j.1475-
2743.1997.tb00582.x, 1997.
Guillemot, J., Francois, C., Hmimina, G., Dufrêne, E., Martin-
StPaul, N. K., Soudani, K., Marie, G., Ourcival, J.-M., and
Delpierre, N.: Environmental control of carbon allocation mat-
ters for modelling forest growth, New Phytol., 214, 180–193,
https://doi.org/10.1111/nph.14320, 2017.
Guillemot, J., Asensio, V., Bordron, B., Nouvellon, Y., Maire, G. l.,
Bouillet, J.-P., Domec, J.-C., Rojas, J. S. D., Abreu-Junior, C. H.,
Battie-Laclau, P., Cornut, I., Germon, A., Gonçalves, J. L. D. M.,
Robin, A., and Laclau, J.-P.: Increased hydraulic constraints in
Eucalyptus plantations fertilized with potassium, Plant Cell En-
viron., 44, 2938–2950, https://doi.org/10.1111/pce.14102, 2021.
Guitton, J., Bonneau, M., and Adrian, M.: Résultats de fertilisation
minérale en région méditerranéenne, Revue Forestière Française,
60, 315–320, https://doi.org/10.4267/2042/25896, 1988.
Hou, E., Luo, Y., Kuang, Y., Chen, C., Lu, X., Jiang, L.,
Luo, X., and Wen, D.: Global meta-analysis shows perva-
sive phosphorus limitation of aboveground plant production
in natural terrestrial ecosystems, Nat. Commun., 11, 637,
https://doi.org/10.1038/s41467-020-14492-w, 2020.
Hyvönen, R., Persson, T., Andersson, S., Olsson, B., Ågren, G. I.,
and Linder, S.: Impact of long-term nitrogen addition on carbon
stocks in trees and soils in northern Europe, Biogeochemistry,
89, 121–137, https://doi.org/10.1007/s10533-007-9121-3, 2008.
Hölttä, T., Vesala, T., Sevanto, S., Perämäki, M., and Nikinmaa,
E.: Modeling xylem and phloem water flows in trees accord-
ing to cohesion theory and Münch hypothesis, Trees, 20, 67–78,
https://doi.org/10.1007/s00468-005-0014-6, 2006.
Hölttä, T., Kurppa, M., and Nikinmaa, E.: Scaling
of xylem and phloem transport capacity and re-
source usage with tree size, Front. Plant Sci., 4, 496,
https://doi.org/10.3389/fpls.2013.00496, 2013.
Johnson, D. W., Sogn, T., and Kvindesland, S.: The nutrient cy-
cling model: lessons learned, Forest Ecol. Manag., 138, 91–106,
https://doi.org/10.1016/S0378-1127(00)00414-X, 2000.
Körner, C.: Paradigm shift in plant growth control,
Current Opinion in Plant Biology, 25, 107–114,
https://doi.org/10.1016/j.pbi.2015.05.003, 2015.
Laclau, J. P., Toutain, F., M’Bou, A. T., Arnaud, M., Jof-
fre, R., and Ranger, J.: The Function of the Superficial
Root Mat in the Biogeochemical Cycles of Nutrients in
Congolese Eucalyptus Plantations, Ann. Bot., 93, 249–261,
https://doi.org/10.1093/aob/mch035, 2004.
Laclau, J.-P., Almeida, J. C. R., Gonçalves, J. L. M., Saint-
André, L., Ventura, M., Ranger, J., Moreira, R. M., and
Nouvellon, Y.: Influence of nitrogen and potassium fer-
tilization on leaf lifespan and allocation of above-ground
growth in Eucalyptus plantations, Tree Physiol., 29, 111–124,
https://doi.org/10.1093/treephys/tpn010, 2009.
Laclau, J.-P., Ranger, J., de Moraes Gonçalves, J. L., Maquère,
V., Krusche, A. V., M’Bou, A. T., Nouvellon, Y., Saint-
André, L., Bouillet, J.-P., de Cassia Piccolo, M., and Dele-
porte, P.: Biogeochemical cycles of nutrients in tropical Eu-
calyptus plantations, Forest Ecol. Manag., 259, 1771–1785,
https://doi.org/10.1016/j.foreco.2009.06.010, 2010.
Lambers, H. and Oliveira, R. S.: Plant Water Relations, in: Plant
Physiological Ecology, edited by Lambers, H. and Oliveira,
R. S., Springer International Publishing, Cham, 187–263,
https://doi.org/10.1007/978-3-030-29639-1_5, 2019.
Landi, M., Tattini, M., and Gould, K. S.: Mul-
tiple functional roles of anthocyanins in plant-
environment interactions, Environ. Exp. Bot., 119, 4–17,
https://doi.org/10.1016/j.envexpbot.2015.05.012, 2015.
le Maire, G.: Code for computing Leaf Size, Shape and
Symptoms traits from scans, DATAVERSE CIRAD,
https://doi.org/10.18167/DVN1/PYAXSS, 2023.
Le Maire, G., Davi, H., Soudani, K., François, C., Le Dantec, V.,
and Dufrêne, E.: Modeling annual production and carbon fluxes
of a large managed temperate forest using forest inventories,
satellite data and field measurements, Tree Physiol., 25, 859–
872, https://doi.org/10.1093/treephys/25.7.859, 2005.
Le Maire, G., Guillemot, J., Campoe, O., Stape, J. L., Laclau, J.-
P., and Nouvellon, Y.: Light use efficiency and productivity of
16 genotypes of Eucalyptus along a 6-year rotation in Brazil,
XXV IUFRO World Congress Forest Research and Cooperation
for Sustainable Development, 2019.
Li, W., Yue, C., Ciais, P., Chang, J., Goll, D., Zhu, D., Peng, S., and
Jornet-Puig, A.: ORCHIDEE-MICT-BIOENERGY: an attempt
to represent the production of lignocellulosic crops for bioen-
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
3116 I. Cornut et al.: Potassium limitation of forest productivity – Part 1
ergy in a global vegetation model, Geosci. Model Dev., 11, 2249–
2272, https://doi.org/10.5194/gmd-11-2249-2018, 2018.
Liu, S., Munson, R., Johnson, D. W., Gherini, S., Summers, K., hud-
son, R., Wilkinson, K., and Pitelka, L. F.: The nutrient cycling
cycling model (NuCM): overview and application, Ecol. Stud.,
91, 583–609, 1992.
Lockhart, J. A.: An analysis of irreversible plant cell elonga-
tion, J. Theor. Biol., 8, 264–275, https://doi.org/10.1016/0022-
5193(65)90077-9, 1965.
Manu, R., Corre, M. D., Aleeje, A., Mwanjalolo, M. J. G., Bab-
weteera, F., Veldkamp, E., and van Straaten, O.: Responses of
tree growth and biomass production to nutrient addition in a
semi-deciduous tropical forest in Africa, Ecology, 103, e3659,
https://doi.org/10.1002/ecy.3659, 2022.
Maquère, V.: Dynamics of mineral elements under a fast-growing
eycalyptus plantation in Brazil, Implications for soil sustaina bil-
ity, These de doctorat, AgroParisTech, 2008.
Marschner, H.: Marschner’s Mineral Nutrition of Higher Plants,
Academic Press, https://doi.org/10.1016/C2009-0-63043-9,
2011.
Marschner, H. and Cakmak, I.: High Light Intensity Enhances
Chlorosis and Necrosis in Leaves of Zinc, Potassium, and
Magnesium Deficient Bean (Phaseolus vulgaris) Plants, J.
Plant Physiol., 134, 308–315, https://doi.org/10.1016/S0176-
1617(89)80248-2, 1989.
Marschner, H., Kirkby, E. A., and Cakmak, I.: Effect of mineral
nutritional status on shoot – root partitioning of photoassimilates
and cycling of mineral nutrients, J. Exp. Bot., 47, 1255–1263,
1996.
Mattila, H., Valev, D., Havurinne, V., Khorobrykh, S., Virtanen, O.,
Antinluoma, M., Mishra, K. B., and Tyystjärvi, E.: Degradation
of chlorophyll and synthesis of flavonols during autumn senes-
cence – the story told by individual leaves, AoB PLANTS, 10,
ply028, https://doi.org/10.1093/aobpla/ply028, 2018.
Nardelli, A. and Fedorinova, Y.: Belgium Is Pushing to Di-
lute the EU’s Belarus Potash Sanctions, Bloomberg.com,
https://www.bloomberg.com/news/articles/2021-10-19/
belgium-is-pushing-to-dilute-the-eu-s-belarus-potash-sanctions
(last access: 21 June 2023), 2021.
Nardini, A., Grego, F., Trifilò, P., and Salleo, S.: Changes of
xylem sap ionic content and stem hydraulics in response
to irradiance in Laurus nobilis, Tree Physiol., 30, 628–635,
https://doi.org/10.1093/treephys/tpq017, 2010.
Nobel, P. S.: Physicochemical and Environmental Plant Physiol-
ogy, Academic Press Elsevier, https://doi.org/10.1016/B978-0-
12-374143-1.X0001-4, 2005.
Nouvellon, Y., Stape, J. L., Laclau, J.-P., Bonnefond, J.-M.,
da Rocha, H., Campoe, O. C., Marsden, C., Bouillet, J.-P., Loos,
R. A., Kinana, A., Le Maire, G., Saint-André, L., and Roup-
sard, O.: Water and energy fluxes above an Eucalyptus planta-
tion in Brazil: environmental control and comparison with two
eucalypt plantations in Congo, IUFRO Workshop, “Canopy pro-
cesses in a changing climate”, Hobart, AUS, https://hal.inrae.fr/
hal-02821072/document (last access: 21 June 2023), 2010.
Nouvellon, Y., Stape, J. L., Le Maire, G., Bonnefond, J.-M., Guille-
mot, J., Christina, M., Bouillet, J.-P., Campoe, O., and Laclau,
J.-P.: Full-rotation carbon, water and energy fluxes in a trop-
ical eucalypt plantation, XXV IUFRO World Congress Forest
Research and Cooperation for Sustainable Development, https:
//agritrop.cirad.fr/594409/ (last access: 21 June 2023), 2019.
Pantin, F., Simonneau, T., and Muller, B.: Coming of leaf age: con-
trol of growth by hydraulics and metabolics during leaf ontogeny,
New Phytol., 196, 349–366, https://doi.org/10.1111/j.1469-
8137.2012.04273.x, 2012.
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion,
B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg,
V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Per-
rot, M., and Duchesnay, E.: Scikit-learn: Machine Learning in
Python, J. Mach. Learn. Res., 12, 2825–2830, 2011.
Pradier, C., Hinsinger, P., Laclau, J.-P., Bouillet, J.-P., Guerrini,
I. A., Gonçalves, J. L. M., Asensio, V., Abreu-Junior, C. H.,
and Jourdan, C.: Rainfall reduction impacts rhizosphere biogeo-
chemistry in eucalypts grown in a deep Ferralsol in Brazil, Plant
Soil, 414, 339–354, https://doi.org/10.1007/s11104-016-3107-7,
2017.
Prakash, S. and Verma, J. P.: Global Perspective of Potash for Fertil-
izer Production, in: Potassium Solubilizing Microorganisms for
Sustainable Agriculture, edited by: Meena, V. S., Maurya, B. R.,
Verma, J. P., and Meena, R. S., Springer India, New Delhi, 327–
331, https://doi.org/10.1007/978-81-322-2776-2_23, 2016.
Reed, S. C., Yang, X., and Thornton., P. E.: Incorporat-
ing phosphorus cycling into global modeling efforts: a
worthwhile, tractable endeavor, New Phytol., 208, 324–329,
https://doi.org/10.1111/nph.13521, 2015.
Rocha, J. H. T., du Toit, B., and Gonçalves, J. L. d. M.:
Ca and Mg nutrition and its application in Eucalyptus
and Pinus plantations, Forest Ecol. Manag., 442, 63–78,
https://doi.org/10.1016/j.foreco.2019.03.062, 2019.
Sainte-Marie, J., Saint-André, L., Nouvellon, Y., Laclau, J. P.,
Roupsard, O., le Maire, G., Delpierre, N., Henrot, A.,
and Barrandon, M.: A new probabilistic canopy dynam-
ics model (SLCD) that is suitable for evergreen and de-
ciduous forest ecosystems, Ecol. Model., 290, 121–133,
https://doi.org/10.1016/j.ecolmodel.2014.01.026, 2014.
Sardans, J. and Peñuelas, J.: Potassium: a neglected nu-
trient in global change: Potassium stoichiometry and
global change, Global Ecol. Biogeogr., 24, 261–275,
https://doi.org/10.1111/geb.12259, 2015.
Seward, P., Barraclough, P. B., and Gregory, P. J.: Modelling potas-
sium uptake by wheat (Triticum aestivum) crops, Plant Soil, 124,
303–307, https://doi.org/10.1007/BF00009277, 1990.
Shen, C., Huang, R., Tang, Y., and Wang, Z.: Potassium nutrition
recover impacts on stomatal, mesophyll and biochemical limi-
tations to photosynthesis in Carya cathayensis and Hickory illi-
noensis, bioRxiv, 425629, https://doi.org/10.1101/425629, 2018.
Silberbush, M. and Barber, S. A.: Phosphorus and Potassium
Uptake of Field-Grown Soybean Cultivars Predicted by
a Simulation Model, Soil Sci. Soc. Am. J., 48, 592–596,
https://doi.org/10.2136/sssaj1984.03615995004800030025x,
1984.
Silveira, R., Higashi, E. N., Gonçalves, A. N., and Moreira, A.:
Avaliação do estado nutricional do Eucalyptus: diagnose vi-
sual, foliar e suas interpretações, Nutrição e fertilização florestal,
Piracicaba, IPEF, 79–104, ISBN: 9788590135814, 2000.
Thum, T., Caldararu, S., Engel, J., Kern, M., Pallandt, M., Schnur,
R., Yu, L., and Zaehle, S.: A new model of the coupled car-
bon, nitrogen, and phosphorus cycles in the terrestrial biosphere
Biogeosciences, 20, 3093–3117, 2023 https://doi.org/10.5194/bg-20-3093-2023
I. Cornut et al.: Potassium limitation of forest productivity – Part 1 3117
(QUINCY v1.0; revision 1996), Geosci. Model Dev., 12, 4781–
4802, https://doi.org/10.5194/gmd-12-4781-2019, 2019.
Townsend, A. R., Cleveland, C. C., Houlton, B. Z., Alden,
C. B., and White, J. W.: Multi-element regulation of the
tropical forest carbon cycle, Front. Ecol. Environ., 9, 9–17,
https://doi.org/10.1890/100047, 2011.
Tripler, C. E., Kaushal, S. S., Likens, G. E., and Walter, M. T.: Pat-
terns in potassium dynamics in forest ecosystems, Ecol. Lett.,
9, 451–466, https://doi.org/10.1111/j.1461-0248.2006.00891.x,
2006.
van den Driessche, R.: Prediction of mineral nutrient sta-
tus of trees by foliar analysis, Bot. Rev., 40, 347–394,
https://doi.org/10.1007/BF02860066, 1974.
Vezy, R., Christina, M., Roupsard, O., Nouvellon, Y., Duursma,
R., Medlyn, B., Soma, M., Charbonnier, F., Blitz-Frayret, C.,
Stape, J.-L., Laclau, J.-P., de Melo Virginio Filho, E., Bonne-
fond, J.-M., Rapidel, B., Do, F. C., Rocheteau, A., Picart, D.,
Borgonovo, C., Loustau, D., and le Maire, G.: Measuring and
modelling energy partitioning in canopies of varying complex-
ity using MAESPA model, Agr. Forest Meteorol., 253/254, 203–
217, https://doi.org/10.1016/j.agrformet.2018.02.005, 2018.
von Liebig, J.: Die organische Chemie in ihrer An-
wendung auf Agricultur und Physiologie, Vieweg,
https://doi.org/10.5962/bhl.title.42117, 1840.
Wang, Y. P. and Jarvis, P. G.: Description and validation of an ar-
ray model – MAESTRO, Agr. Forest Meteorol., 51, 257–280,
https://doi.org/10.1016/0168-1923(90)90112-J, 1990.
Williams, M., Rastetter, E. B., Fernandes, D. N., Goulden, M. L.,
Wofsy, S. C., Shaver, G. R., Melillo, J. M., Munger, J. W.,
Fan, S.-M., and Nadelhoffer, K. J.: Modelling the soil-plant-
atmosphere continuum in a Quercus – Acer stand at Harvard For-
est: the regulation of stomatal conductance by light, nitrogen and
soil/plant hydraulic properties, Plant Cell Environ., 19, 911–927,
https://doi.org/10.1111/j.1365-3040.1996.tb00456.x, 1996.
Yang, X., Thornton, P. E., Ricciuto, D. M., and Post, W. M.:
The role of phosphorus dynamics in tropical forests – a mod-
eling study using CLM-CNP, Biogeosciences, 11, 1667–1681,
https://doi.org/10.5194/bg-11-1667-2014, 2014.
Zanne, A. E., Westoby, M., Falster, D. S., Ackerly, D. D., Loarie,
S. R., Arnold, S. E. J., and Coomes, D. A.: Angiosperm wood
structure: Global patterns in vessel anatomy and their relation to
wood density and potential conductivity, Am. J. Bot., 97, 207–
215, https://doi.org/10.3732/ajb.0900178, 2010.
Zhu, Z., Arp, P. A., Meng, F., Bourque, C. P. A., and Foster,
N. W.: A Forest Nutrient Cycling and Biomass Model (ForNBM)
based on year-round, monthly weather conditions: Part II: Cali-
bration, verification, and application, Ecol. Model., 170, 13–27,
https://doi.org/10.1016/S0304-3800(03)00284-9, 2003.
Zhu, Z., Foster, N. W., Arp, P. A., Meng, F., and Bourque,
C. P. A.: A test and application of the model ForNBM
in a northeastern Ontario jack pine (Pinus banksiana
lamb.) stand, Forest Ecol. Manag., 193, 385–397,
https://doi.org/10.1016/j.foreco.2004.02.003, 2004.
https://doi.org/10.5194/bg-20-3093-2023 Biogeosciences, 20, 3093–3117, 2023
